{
 "cells": [
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style = \"font-family:Georgia;\n",
    "              font-size:2.5vw;\n",
    "              color:lightblue;\n",
    "              font-weight:normal;\n",
    "              text-align:center;\n",
    "              background:url('./text_images/Title Background.gif') no-repeat center; background-size:cover)\">\n",
    "    <br>\n",
    "    <br>\n",
    "    Principal Component Analysis (PCA)\n",
    "    <br>\n",
    "    <br>\n",
    "    <br>\n",
    "</div>\n",
    "\n",
    "# Introduction\n",
    "\n",
    "In the previous lessons you've learned the core idea behind **Principal Component Analysis (PCA)** and leanred about eigenvectors and eigenvalues. Before we apply PCA to Risk Factor Models, in this notebook, we will see how we can use PCA for **Dimensionality Reduction**. In short, dimensionality reduction is the process of reducing the number of variables used to explain your data.\n",
    "\n",
    "We will start by giving a brief overview of dimensionality reduction, we will then use Scikit-Learn's implementation of PCA to reduce the dimension of random correlated data and visualize its principal components. \n",
    "\n",
    "\n",
    "# Dimensionality Reduction\n",
    "\n",
    "One of the main applications of Principal Component Analysis is to reduce the dimensionality of highly correlated data. For example, suppose your data looks like this: \n",
    "<br>\n",
    "<figure>\n",
    "  <img src = \"./text_images/1.png\" width = 80% style = \"border: thin silver solid; padding: 10px\">\n",
    "      <figcaption style = \"text-align: center; font-style: italic\">Fig 1. - Highly Correlated Data.</figcaption>\n",
    "</figure> \n",
    "<br>\n",
    "\n",
    "We can see that this 2-Dimesnional data is described by two variables, $X$ and $Y$. However, notice that all the data points lie close to a straight line: \n",
    "\n",
    "<br>\n",
    "<figure>\n",
    "  <img src = \"./text_images/2.png\" width = 80% style = \"border: thin silver solid; padding: 10px\">\n",
    "      <figcaption style = \"text-align: center; font-style: italic\">Fig 2. - Direction of Biggest Variation.</figcaption>\n",
    "</figure> \n",
    "<br>\n",
    "\n",
    "We can see that most of the variation in the data occurs along this particular purple line. This means, that we could explain most of the variation of the data by only looking at how the data is distributed along this particular line. Therefore, we could reduce the data from 2D to 1D data by projecting the data points onto this straight line:\n",
    "\n",
    "<br>\n",
    "<figure>\n",
    "  <img src = \"./text_images/3.png\" width = 80% style = \"border: thin silver solid; padding: 10px\">\n",
    "      <figcaption style = \"text-align: center; font-style: italic\">Fig 3. - Projected Points.</figcaption>\n",
    "</figure> \n",
    "<br>\n",
    "\n",
    "This will reduce the number of variables needed to describe the data from 2 to 1 since you only need one number to specify a data point's position on a straight line. Therefore, the 2 variables that describe the 2D plot will be replaced by a new single variable that encodes the 1D linear relation.\n",
    "\n",
    "<br>\n",
    "<figure>\n",
    "  <img src = \"./text_images/4.png\" width = 80% style = \"border: thin silver solid; padding: 10px\">\n",
    "      <figcaption style = \"text-align: center; font-style: italic\">Fig 4. - Data Reduced to 1D.</figcaption>\n",
    "</figure> \n",
    "<br>\n",
    "\n",
    "\n",
    "It is important to note, that this new variable and dimension don't need to have any particular meaning attached to them. For example, in the original 2D plot, $X$ and $Y$ may represent stock returns, however, when we perform dimensionality reduction, the new variables and dimensions don't need to have any such meaning attach to them. The new variables and dimensions are just abstract tools that allow us to express the data in a more compact form. While in some cases these new variables and dimensions may represent a real-world quantities, it is not necessary that they do.\n",
    "\n",
    "Dimensionality reduction of correlated data works on any number of dimensions, *i.e.* you can use it to reduce $N$-Dimensional data to $k$-Dimensional data, where $k < N$. As mentioned earlier, PCA is one of the main tools used to perform such dimensionality reduction. To see how this is done, we will apply PCA to some random corelated data. In the next section, we create random data with a given amount of correlation. \n",
    "\n",
    "\n",
    "# Create a Dataset\n",
    "\n",
    "In this section we will learn how to create random correlated data. In the code below we will use the `utils.create_corr_data()` function from the `utils` module to create our random correlated data. The `utils` module was created specifically for this notebook and contains some useful functions. You are welcome to take a look it to see how the fucntions work. In the code below, you can choose the data range and the amount of correlation you want your data to have. These parameters are then passed to the `utils.create_corr_data()` function to create the data. Finally we use the `utils.plot_data()` function from the `utils` module to plot our data. You can explore how the data changes depending on the amount of correlation. Remember the correlation is a number ranging from -1 to 1. A correlation `0` indicates that there is no correlation between the data points, while a correlation of `1` and `-1` indicate the data points display full positive and negative correlation, respectively. This means, that for `corr = +/-1` all the points will lie in a straight line.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
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UmML2LcNllqGVzFJYtRq10s3EkyTQ2gTFqC0Cwx02dWymoePSGal4fGXrlrHdsKgYdHd31xQFoVB3xe1GIHqlRIVSvvSVb2JuLom/uOod6OkJ4we3/xgvvnig5nFOuFwucJz+OwFfRy25XE4fo4dvb905w2KVyVT+rdWwZBn71eKW//ountmzD9d96L147avPRLfYBVHswmtffSY+9MFrIUlZ/Pf/fH/h+kVLnvG+lJIpbvdRUC+xilnK+K1OYve+Uezaux+jh45i1979ixaiFHu2ciCL2iI4eeuJ2P30s/jTk0/jrFefXfdxhisrHp9Df3+5G3N2NlHcz74A12O4cRJywW5dwNWyUv30Zw/jsT8+idNOfRneeflbsHnzMD71DzfhP7/wdXz5i/9clhSxFBhjNMZci6WKUfN6vYhEwpiZmcXsbLwsTm18YhIA6i4j8sc/PQkAeNkpW8s+2/4yfduLowuCeGCgFy6XC5OTx5DP58vcz+PjjV2fII5Hlip+qxMx7se458XcH8WerRxIqC2C8859Le744d34xa9/j7e+9WKsL2b1VUJRFFPkbNq0ES+OHsTTz+xFf3+vbb/x8UnMzMygrzfa0obw4XAQ3d0ixo46B55PTEzhm//1HXR1BfCR698PADh1xym48IJz8ZP7H8St374D7722dh21xXL06ATErgB6esJ17b9UMWqALqB+8cvf4fEnd+P8c8+xffb447uL+5S7sCuhFDN555LJsiSJuTldnFozYTmOw5Ytm/Hss89hz7PPlV3n8See0q+/vVz4EcRqYTVZhuoJ/m8Eij1bGZDrcxH09kbxriveBkVR8Q+f+Xe8sP+livs9/sRufOrTnzN/Pv+8cwAAP7j9LszNLXwx8vkCbvnv76JQ0HD+ea9r6VgZhsG2k09CMjlvWmKs5PMF/Mfnv4ZsVsaH/uo9iEQWrEfXvvtKDAz04a577scze/aVHXvhxVfiwotrx57Vw+TkMcQTczjllK11x35ddeXbcf+932voT71ceMG5AIDb77gb86mUuX1qKob77n8QHMfhvHNfaztmbi6JI0eO2p4toFtgAeB73/+RrVF6Pl8w6+GVirGLitf/9nfuRC6XM7e/8MIofvPbP6C7W8Srzjq97vshiOMNwzJk5Xi0DC2Vi3cmnsSBscnjbr6OJ8iitkguf8db4OVc+Oa3bsdHPvZ32LJlM0ZOGILg9SKemMOeZ5/D+PgkRk7YZB6zdctmvP1tF+OH/3svPvChT+Dss14Jr5fH40/sxqFDR3Dy1hPxtkvf1PKxnn3W6Xjk0T/iiV1Pm6UdDG6/8y7se24/XnfOq/DqV51h+8zr5fHxj34AH7/hM/jCF7+Br375JtMipBUj2l2u1mj+J3c9Y461E9i6ZTPe+pYL8eO77scHr7sRrzrrlVBUFb/97e8xP5/CB95/dVlXgnt/8gC+9/0f4corLrVZ7t59zRXY99x+PPyL3+LFFw/gjFdshySreGr3Hhw+chSi2IVr/uJy27le+5oz8ejv/4jfPfJHXPfhT+L000/F/HwKv/nt71EoFHD9h97rmJVKEKsFq2UoyOexe3Ss5ddwsjwtl0VqNbl4CTsk1FrAX15zOXbsPA0/KTZlf/Ch30BRcujq6sKmoQ247G0X4/Wve5XtmPdccwWGN23Avfc9gF/88rdQ1Tz6+9bgL656By5964Vm8H0rOfus0xEKduPhX/xWL7BbZP+LL+EHt/8Y0WgP/ur/XFPx2JNOGsFlb38zbr/jLtx8y234yPXvAwAcOHgYgC4oWsHDv/gNurvFjhFqAPCX116FoY3rce99D+CnP/8FXC4Gw5s24m2XvqmhpuxDG9fjK1/8F9z5v/di11PP4Ef3/BwAg2hPGBe/6Xxc9vY3oydid/cyDIMb/uY6bDnp53jgoV/j3vt+Dg/HYdvJJ1FTdoKwYGQlnrKhvpCJRnByObbaFVmN1eTiJewwhkVkpdM/uEG7+rq/bek5X3z6Ubz53J2I1qiTZu3Z2OncfufduPXbt+MrX/yXivXWGuXue36Gm2+5DV/7yuewYUN5jF4jc3PgwGF88Pob8edXXYYrLn/rosfW6SzHe/PkU89g75iCdUMjS3qdpeCUDWE8c2i23cPoSGhunGn13ERCInZsLf/+HBibwNBgeSLPrr37l8zCtVhhSO9NdZZ7fj534/uf0DRtZ639KEZtlfHWSy5ANNqD2757Z0vO98yefXjl6adWFGmNctt370RPTxiXvuWiFoyMIAhi8Ti5HHsjlcsrLWUPzFaX6CBWBuT6XGV4PB58/GMfwNPP7EU2m627yboTf/fJj7ZkXNmsjOHhjXjLJReAb3P9tOOK48NgThBtw8m1ODWTwNBgeQ3FpXZFUuHZ1QcJtWowLuTzx187klO2bcEp27a0exg2vF4e77ribe0exnGHouZbluhBEKsRp3pjo4fGEfAJVIeMWHJIqFXBxXqQSqXbPQyCaJrEXAoevqfdwyCIFY1TvTGqQ0YsB/SrdhW6Qr3Yf+BIu4dBEE2hKAoOjk0hGInW3pkgiKo41RujOmTEUkNCrQrhnl4cPBLDzEy83UMhiIbZ9/yLYIUQOI5i/giCIFYqJNSq4GZZ9A69DHff/2tMTEzheCllQhzfKIqKp/fsw6NP7MfgcH3trQiCIAi9HMvQYN+iOz60EopRq0FkTR8YhsG9Dz8OjyuPTRv6EfB74bYEaIf8POJpuY2j7Fxobpxp5dxomgZFzSMxl8KBw5NweYMYOvmV8ArUtYAgjkdqxcY1GjtHsXaAIPDYMThk/ryUBYwbgYRaHYSjvQhHe5FJpzAen4Y6m7NZ14b6OByYXBkFb5cbmhtnWj03LrcbHj6MTdtPAuchdyfRmZAgWDy1Ct82Whh3OTssdCqRkAjO7bZtM3qptvs9JaHWAD5/AD5/oGz71g1h5P1U7bkSNDfO0NwQK4lWCCwnQUDirX6qNWefiScbbt5e63yrhU7upUpCjSAIgqhKKywuToLg7J3bIPD8os69mqglKKp9DuQaPt9qIZnOYKC7XMx2Qi/VtiYTMAxzIsMwT1n+JBmG+QjDMGGGYR5kGGZ/8e9QO8dJEASxWmnUQuNEJUEgeHn0l/RSbubcq4lazdkbbd5Ozd51ZuJJKCUF7julgHFbhZqmac9rmvZyTdNeDuA0ABkAPwZwI4CHNU0bAfBw8WeCIAhimaluoamfSgs/7+EgK8qiz72aMDolWLEKilqfN3q+1YQkyR3ZS7WTXJ9vADCqadohhmEuAXBOcfutAH4F4IY2jYsgCGLV0iqLS6VWTBOxGZvbs9lzrzZqxfU1GvdHcYILdGIv1U4Sau8E8P3iv3s1TZsAAE3TJhiGWdO+YREEQaxenHpdNrOYVRIEleLfOm2hbJalFD+1BEWjgqMTBQqhw3RCEVeGYTwAxgGcrGnaFMMwCU3TgpbP45qmlcWpMQzzPgDvA4BIpOe0L33168s2ZisC74YkH3/N21sBzY0zNDfVoflxph1zw7JuuF0u5AsFqGprr93Kc3fKeyMIvK3cg5LPQ5LaW1OyU+ZmKWjFO7Tc83PVFZc9oWnazlr7dYpF7QIAT2qaNlX8eYphmP6iNa0fwLFKB2madjOAmwGgf3CD9syh9pQ6OGVDGO26dqdDc+MMzU11aH6coblxphPmJhISbYVTAUAAMLp3f1utVp0wN0vB9i3DiLSgDlynzk+ntJC6AgtuTwC4B8DVxX9fDeDuZR8RQRAEQTRBqxIwiNq0Kiu5k2m7UGMYxgfgPAA/smy+CcB5DMPsL352UzvGRhAEQRCNUi0Bo9lekp3Yg7ITWA2iuO2uT03TMgAiJdtmoGeBEgRBEKuQlZyF6JSAMdgXbapwMLV4cmY11IFru1AjCIIgOoflFkiVrnc8CJPSDFcA2LF1xLZPPa2aqMVTdVqZldypkFAjCIIgANgFkuDlIWX1AqBLtehVEmRjk7HjRphYS14MDfZV3KdWqyZq8VSb470OHAk1giAIwma56e0Jwe/zAtDLTBw+OtVyi5aTpciJlS5MmnXRrQbXXis4nuvAtT2ZgCAIgmgvkZCIE4cGIXh5CF7eFGkAwHPckmTRtaIF1Uqi2VZN1OKJIIsaQRDEKsZwPwoCj/5ouOxzoxdnoxatWq4oJ+E1NhkDgOMy5mj3vlEMbxhAbySIqZkERg+N133c8ezaI6pDQo0gCGKVYnU/SpKMtJRFd1cAgAZVzSMtZc1q+o1YtOpJBqgWBD4TTx6XwsQ6L0ODAgI+oW6X8nK69o7HuV/JkFAjCIJYpZS6H6dicSRTGfAcB1lRTJHWiEWrkSzFapaiVgmTVouOZs+3UrI3j4eM2+MNEmoEQRCrlEpWMkmS8egTewCgKUHSaJbiUlqKSkWHJMsYn5wuu6d6xZdTlmo9x66E7M2VIiZXGyTUCIIgVim1alA1szh3SpZiqegwMlnDQRGSJJuWomoWpNI6aKUiZtuJQ1g/0AspK5cdW0qnzEs1WiUmyXXaWkioEQRBrGJaHajeKQVIraLDmsnKcxwkSUY0HMTwhgFHC1JpFwFB4G0uYUHg4Re8kGXFFGrVrE+dMi/VaIWYJNdp6yGhRhAEscqxuh9bIdqWK0ux2jWs4oL3cOa/jSxWAOiNVK7bVirSentC6Bb9ABioqoq0lIUs6+eRc4rt2GrWp07P3lysmCTX6dJAQo0gCIIA0FpryFJnKdYaq1V0GGLKmsUKAFMzCQwNClWvY1jjVDVvbvMLXuQUFelM1rSmGdSyPi1H9uZixOBixORKiMNbiZBQIwiCOA5YrKVmJVlDqo3VilV0zM4lIfC8+VlsVq9jFvAJZQkHwEILLas1biI2C2i6hW7/wTHzutZzNjtXrbK0tUJsNysmV0Ic3kqEhBpBEESddKrbqhWL80qyhlQbK5CzbTNEx4GxyYrPzyrmBvp6IPA8BJ6H2OWDGPAhmdJFhtUaJ2VljE3GWlbvrVWWzHaL7ZUQh7cSIaFGEARRB50aJN2qxbkea4iTKFluAVttrAGRrVmbLRISMTTYZ35u7DNssbhNxeJ6n9PxqYrWOGtm7GLuuZXiqhPEdqfH4a1ESKgRBEHUoN2Wimq0anGuZQ1xEqrtELDVxjrc248dg0OO43Eab6V5lCQZyfn0koqPVoqrTnE9Hs8N0tsBCTWCIIgadIKlwolWLs5OgqRUqAoCj5GNg3C5XIgE7XFhyyVgK401EhLBcxyCYgByTi+bYR1PNcFdax6XSnwshbgy4usAcj0eD5BQIwiCqEGnWCoq0eq4oEqCxCpUe6Mh+AW9JlnAPwxFVTEVi5ftv1h3YD3Wq9Kx7tg6gkJmFuFgFwAgncliajpujqea4D4wNlk2j5Ism8csldhp1fOzWQoZ/a9de/eTSDsOIKFGEARRg04Pkl7quCBDkBpFXg3SmSxC3QEIAm8re7EYAdusKzUSEiEIPKyX9vu8CHV3Qezy12U1q5RYMLxhbUPjaAYn62C9z7PUUmh9FsTKh4QaQRBEHSylGGrFeZcyLsgQqiMbB81t6UwW8bl5eDjWrPYP1C9g63GxAvW7UkW/D5IkI69p5ja/T4BWPEc0HERsNlFTcFdKLGhkHM1ifX6NitVOds0Ti4eEGkEQRJ0shRjq1GzSUnbvG0UqI2HH1hEz/gsApqbjODA2gUK+ULfQbCSgH6hPcLjcLgTFAKaSMUzEZiEGfGBZFpPHZs19ouEgdu3dX7OReiPjaLV4b0as1puxy3u4jkiAIRqDhBpBEESb6ORs0kpUKhBrFI6tl8UE9DthCD/ew4Fj3RADPsiygjktVdY5wIhHqza/9Y7j7J3b0B+NmMK1FSK7GbFab8aulJjCjq2DHfvLAFEZEmoEQRBtotNcVvVYh6q5gOs5vtGA/lquVKvwm5qOQ1HzkGUFo4fHyzJSgfri52biSUiyXCbCAJj1104aXo+TRzaax6QzWXM8i3l21URitfmtN2MX6OxfBohySKgRBEG0iU7KJm3EBVvJBVzv8Y0E9NfjThT9PgheHryH00VVooBEMoXE3DwKhUJTCSDbtwxD4HnIigLew2F2Tj9mx9YRCF4eYsCHbjEAVVXNY/w+r/7ZIkW2k3WstFF8pfm+oyicAAAgAElEQVStlbFbup2E2sqAhBpBEESbaDSbdHjDAHojQeRSMy0dx2KsLpGQiMG+KNYP9NrcjE7H13PPjcQCDvT1oH9N2Pw5Oa27YZPpjGPbqNLxl2ZbGmOTJBmSJCMcFBHuFiEGfPD7vPDyHvh9AhRVRXI+bZ6L93AtEdmlYhXQRaKVep9PJ/0yQDQHCTWCIIg2Uq8F6c3nnoW+qC5IXnxOwpvPPQv3PPRoS8bQrNXFsKIFxQDCwS6zblmt4xuxmlXbLxISIfA80lLWLBvidjGQZLmuFk+VrIBW4WXAcxx4Dwe/zyhNwsDFMOBYFizLmpa1idhMy6xU1nEPDfYBgN1ymJXrsop1emkZojYk1AiCINpMLQvS8IYBU6QZ9EXDGN4w0FAgvxPNWF2slidZUQAA3WJAPy6VgZSV4XK7bD01rdRjNavlTjUEptGXk+c4KGoe47HpquctHb9BNBxEKiOV7Wu4QAG95IeHY8G4GCCvlwKZTcxjIjaDRx7fsyQlXJLpDHp7QhahqMfE7dq7v67jDWE81CPguQ4rgkt9QWtDQo0gCGIZWMyC1BsJOm5vhVBrxupitcJJkgyOZRHwC2DdLvh9Xqhq3rZ/rUzDai5Ig1J3n1VIGm7KQqFQl1vPyYpYyBfK5uLw0SkE/AK2bzkBHk5fNtOZLORcDnPJNHbt3Y/RQ+NLW2qFqfFzDWbiSQyIbEeJoZVSmqbdkFAjCIJYYowFyXBdGdaXepmaSWCbw/ZWUW91fGOby+0yjxUEHoqqYj4tYS6ZQk5VERIDtp6T1WKq6nVBAnZ3aiWBqeTzdYmRalZEp9i2SFDExsE+qPkCVFU1Xb2FfGFJsytFv89mNZQVBZJUn+uzU6Fs1PohoUYQBLGEGAuS1XVl9KKsV6yNHhrHySMbbe7PydgsEsmUo2vRaSzVrHq1quMDsG3zCTwykgye092Cc8kUpqbjCBZdoLyHsyUYOBWMrdcFCZQLrFKBOSDWt6zVsiJWcs0+8sQeaBpscWLGmKwWOmssWSvElHHPhtWwdDuw8lyIlI1aPyTUCIIglhDR70OouwuRkAg1nzddgv3RSEPWg3seenQh6zOdwUx2ypYJKMkyxienHRfqam6metyO69f2AhpswkvT9OtKMdkmXIyYNTmn2M5RyYrViAvSyR1rFVUDYrjscydqJTWUfjYTT+Lw+FTVMZXGks3OJXFgbLLuMVWi3oK21s863YVI2aj1Q0KNIAhiCTHKRwhevXdkTlGRzkiQlcatLaOHxpFIpjDc68f6tb2mdaU3GoJf8CLcLVaskF/NzVSpPpdT5iOgCzXBy6MvGgbHucF7OCSSKTCWmClJkjEZm7WJOieR1YwLspU4JTU4iR8ncWcUybUF/EtZCDxfJsibuafjraAtZaPWT9uFGsMwQQC3ANgGQAPwHgDPA7gdwEYABwG8Q9O0uMMpCIIgOhKjfMR8WjKFmodjkVBVSJLcsPXAEA+5+Wn0R8NIS1kkUxmzNIXhaixdqJ2sVqUiDaie+QhNtxh1iwF0+QUAgJTNIZFMISPJZT0/6xEk1Rbsdrnzaokfq7izjnF8chrhoGiLIwPs7rxa1q9q93y8FbRttLjxaqXtQg3AlwD8TNO0tzMM4wHgA/BJAA9rmnYTwzA3ArgRwA3tHCRBEESjiH4fBIHHfCoDD8eC93BQ8wXMp6SGrQdW8aBpelkIQ6AZWF2N1oW6UUFYLfOxf00YbDGRIKeo4Fi3mTRQyBdsbr56C9dWWrCbdeexrLuhuL1K1Ct+SscoyXJZHBmwMP+1BGAz97zSXYiNFDderbRVqDEMIwJ4DYBrAEDTtByAHMMwlwA4p7jbrQB+BRJqBEGsMAb6etBfTADQNA3zaQnzqYxZzqERDPEgCDxy8wwUNQ+OdQPAQtFVi/vRulA7Wa3GJmNlwsE41nr82GQMM/Ekhgb7EA7qFfq7uxZaKBmWvHrEgZMFpdRK1Yw7b/uWYfhcMgaH1oPnGs+uNahH/FQao8DzkGQZAs+b26yCvJoABNDUPZML8fin3Ra1TQBiAP6HYZjtAJ4A8GEAvZqmTQCApmkTDMOsaeMYCYLoYDrVdWJWzc9kzbgljnVjIjaD0UPjDY87mc6YsWjpmQlwrFtvYZTKwMOy4DjWdIfuef5A2Tmd3Ez19JUEdEGQTGdsFiPDoifnlLrEQSWL0dhkrGxMzbjzDOGkpGdMcdxodq1BPeLHaYxGQkelZ2sVetZSG6VZo1bqcWFan63L7TLLhXTS94FoHsYwobfl4gyzE8AfAJytadpjDMN8CUASwHWapgUt+8U1TQtVOP59AN4HAJFIz2lf+urXl2nkdgTeDUnO195xFUJz4wzNTXXqmR9B4MG53ebPSj5f5nZqF7yHM6vZu1wuMAwDTdPMiv2Njptl3RADfrhdDLLZLLxeLzQAqppHoVCAy+XSa5tpQFqSIMuK7Vi3y4V8oVBWiLb0cwDwefmyfTJZGaqat825y+VCoVAwP6s1/tLzsiyLQqGAQvG6xjxU2tc6hkrwHg6Cl0deVeD1LriE1XwB8+lMzfFVGi9XLG6rKGrZ8c2MEdDfWcHLw13MvsgXNEiyDEVRmzpf6bmrvVf0f051lnt+rrrisic0TdtZa792W9TGAIxpmvZY8ecfQo9Hm2IYpr9oTesHcKzSwZqm3QzgZgDoH9ygPXNodjnGXMYpG8Jo17U7HZobZ2huqlNrfiIhETsGh2zbBACjHdIiJxISsWPrYNn28eQEhgb7bdvqGffQYB8GNw5ADPgwdvBF+MP9phBMJFOmtQ3QWxrtPziG3ftGcfbObeiPRszg9lpxT0ODfYj09S6MrWj52X9wDM+MVi7nUQ9l5/Xy6F8TxmxiHolkqmQeZitb32aTVUtpvO6MkzA7eRgnnHSyuX3i2CyOzL6EA2OxusYJ6Ja/SMm1jXsv3a8spmx0rOq5IyERZ506ZKvFxgWAXXv3Y7BPbPh81vPW+j7Q/znV6dT5aatQ0zRtkmGYIwzDnKhp2vMA3gBgb/HP1QBuKv59dxuHSRBEB9Lp2W6l7jNB4CFJMgI+oeL+tcZtlPkA9MbjYkAXLND0c1sTC+Scgmg4iPNfvRMbiw29Ab1cBICqbjGre84q/tYP6CJr977RpgLAS+O+DJFp1FwzMOah1FU72Be11Y0rFZwz8SQmYjOw2qTSmWzdsXMGkZCI9Wt7bZmbTrFizWQtin4fpKxsK11ibF9MFmSnfx+I5mm3RQ0ArgPw3WLG50sA3g3ABeAOhmGuBXAYwGVtHB9BEB1IJ2W7lcYHGYussfDu2DqiFx+CLnjELr0lUL3jNuPdpKwpnPw+Lw4enUQqLWFk44LlzhAnglev32XFL3ghCHzVxdsQmOvX9prXMs65mPpcpcJVzilIS1nHDEnjmHr7fgJ6LNqZW9diNjFvWqsaDazfsXXEjHEDdHE7FYvb5qxSIdx6qfXeNpsF2UnfB6K1tF2oaZr2FIBKPto3LPdYCIJoH41aEjol281wf5mB/sX+j0anAKMnpmFBkbIyxIDPtLDVM27DWmL0e1TzBUzEZjE+OY0DY5NIZSTs2Dpi6w7AezikpSw8XMB2Lp7jai7ehqWK5+ytkoyxNDvHlaxk9Ty/RqxFqbSEX/5hV1NWqeENA+jtCYFl3VDVPFiWRSQoIqeoSO7V52yxXQCW6r3tlO8D0XraLtQIgiAqLX6FTO0a1+0umGlYeqyuR7/Pi3UDUXAsi3C3aCYVTE0v3M/UdNzsAFDPuK3CSpJk5ItB4sb20UPjCPgE2xxOxGYg8Dw8LGurlj8Rm6lrnqqV7lgMVotRvUVtG7UWNWOV2r5lGCMbB+H3ecF7POgOcCgUk+1CYgCDfVEAzZXQKGWp3tt2fx+IpYGEGkEQbcXJrTWTq2+RaWfBTMPSY7RXAvRMRi/vQVbO6QHjioJwsMssCmtg1CarB6M9kZkUkCiv3j82GSsrdbF9yzCAhSbhjdQVWy4LTWlJjkrnb+VYqrVhsvYo9fIccjkFck7BRGy2omg1aMbKuFTvLRWQPf4goUYQRFtxcmu5Xa4lu2arrA6GRccaEM+6XVDzeoq/4TZMS1mzKCzQuMjYvmUYAs9DzingPbqlZ/e+0ZpuuMVaWJbDQlOvK7EVY3G6lvEOSpL+rCJBEYWChny+gLn5dM3SKcsVB0bWstUJCTWCINqK0yJn1PRqNYuNMXLCCPSfT0vgWLcZgA/osWVGH8xGC5JaLY5GtqCLYTC8YaAuN1ynWliMhvDW5vJAdVdipXupV7xUS0iwvoNTsThyior+aBgTsVnEE/PmZ2OTMfM4g+WKA1tMj1BiZUNCjSCItuLk1io0WKC0HpptTVQJ28Kp2cXYQF9PWRuh0UPjTYlEJ4tjb6SyK65W9f5GFvOlErXGeYNiAAO9PXC7GSSSKUzPJvVkizpdiY3ENlrn0XAFyzkFot+HA2OTtncwnpiHLOegAQiKAciKgsNHp2xZqMspipaiRyixciChRhBE26nk1jplQ7j2gQ3SqlpTpQunYTlLJFOYiSdxYGyy7H6aFYlOFkdJVjDQGzVrfdXa32kxdxId1eqJAWhaqFjnYaA3gp6wCIZh0N0VQF9PGIfHj2HX3v0NncegWmyjMS+9PSFbcsXsnP68KmWkGrXjUNLAZ7mtlEvRI5RYOZBQIwiiI1jqxS8SEiF2+W1lMQwajTGqR/CV3k+zIrGSxdHlciEi6hml4WCXWevLyQ3nJGrO3rmtzPJnWGKc6olZi86WHlN6zUpizpiHUHcX/D4vGDBgGAYuFwOPh4PfoSBw6XnFLn/Fz6vFNgoCj27Rb7ZkSktZCDxviprSum3WwrSLFT+VhHul2nuVqJb1Wuu9sl6XWJmQUCMIYsVSrwvKak0S/T6IgYWCs83EGDVTXLSZYypldLrcLvQFdDEyNR033XgHxiYwemi84nkqLeaCwCMoBsz2TcCCGAmKgWI9MRaqqgLQi+WGgl2ABniKPTCTqUxFAWO2rbIUnTXEnHG/fp8XHo4DGJgWK03TkFMUR/G6fcsw1g/0gvdwYBgGHg9rKxwsCDzSHIvtW4ZtWbXG89ezc/UemxOxWVOwlxazPXFosCxLt3S/Rii1ZvoEHhlJNq17VqFdSfQ2k/WaTGfKrpucqfx+EJ0NCTWCIFYcRrV/62JazbJjXawMcRObTTRUIsNKMwtno8c4uSqHBvugN2/RMaw+hbxz8kUlMWgUsy1lx9YRBMVAsZ6YXgMunZHAsiz6omHwHs60WuUUFcem7VX7z965DSePbDTPl87Y21YZ89AXDYMpNiYvaAXk8wUwDAM1n6843khIxLbNQ6bbkmVZ8B4OOUVFPDGP3mgI3QE/0jMTOOWkLdgmDWHP8wds9eBkRTGFp9WdaVzPmHNB4NEfDZvFi6vNozG2aj1Irc9R8PLoi4YRT6bMezE6RlSz2jm5qZ3eK6DcJcq53eQSXYGQUCMIYkWxfcsw1q/tNd1yxmLqtMhVsiZJWRnJ+fSiFqxmykXUOsbqDquWoTjQbW8NBdhFRKUWR6WLuVEQ14og8IAGU8DpAs0NlmXBut1wu10I+ATT8uXhWHSLAbP7QiQkoj8asZ3T7/NC8PLmczAshAAQjQTR5RdMwZbLKZg8NltxLgf7ogvCxieYVr2A4EVWziGXU82yKIAuftav7bWdwyi/4Re8ZrkUaz06M7vW2K849mqtqGoF8pe+f0aPU2tvVkAXzpJUPZHCKTyg0ns1ZOnxaoV6f648SKgRBLFiMBZTa4FZ62JaaRFayh6I9cbVOfWGdGqnFBQDZd0MAJgZikqvH9ZILquIcBIOlRbz0n0ZAJ5iNmQ6ky0KIwas24WsLCModsHlYsAwLtP6paqqac0T/b6yJuuALk4G+nowbBGGkizjmedeQijYhWBXAGpexfRssmYiAcuypkgDdKsez3HweMqXM+t7YmC04Tp8dMpmUS0VVMZ+M/EEnj8w1lDsn/UXhtL3zBTBJe29jHlr9r0sfRep9+fxAwk1giBWDMZiWioGDOtIpUVoMVXtW1GGwUk4WbcbjdINYebUzcC4P0mSMTM2gd5IEFMzCTM2zSocBIGHGPChNxpCKiNh9NB42WJuFW8DfT0QBB7hYBcA3VI5cWwWkZCItLTgvjRclIWC7q6MJ1PmuJLpjM1qZY47lS633vE8JFkGEjBrlUmy7NihYGwyhm3SECLBBWtiTlGRTOnXNixVVmRFqVj77PDRqTI3eaV3R5JkR5EG1J9UYn3/pKyMydgsMpJstvcymtO3siZbpfdeyefJmrYCIaFGEMSS0+pOAKViQM4pVRe5ZtyUrahN5WRxKS1Wy3OczTJo3J9TNwNB4NEb6QcADA0KCPgEW4X93mgIayIh0/L0+jNPNfcpxTjnMM/b5tXv8yKZymD/wTEIvJ54kJUVuN1uuF0u5AsFFAoFyHKuTJQYY+Q5vW3V+OQ0hjesLbv2+OS0mbk40NeDcFA022SViqmZeBJ7nj+AzZvWFd3ejK3R/excEhvXLrj70lK2odpnzQbs17O90vvnlPVZz3ta77tcet0BkZb8lQg9NYIglpRWFuO0LqaGa0qSZOzau7+m+Gqk/Ee9Nc9qxZs5ZQ+WFqs1LIRWYWYtoFval5JzuyuOLZnO6CUougI29yDHubF+oNcxecJqGZqKxREKdsEveDE7l8Rzo4exY+sIGIZBOiNBzinweXnkCwXIuRw0TX/GxjN1EiWVsN7XWYN9pvBmWRb90bBpCTTYvW8UY5MxvPE1p6NbDIBhgP41YUzGZvHQI0/gudHDGO7147Gn9pXdaz3Pv1FB34i4K71+pfHU811p9Ptkvc6A2PrahMTSQ0KNIIglo5WdAAyWo/9kPS6tagumUUZC7PKhu8uPuWTaFm82NZPA0OBClJlhybJmYRrdDBoZ24GxSUiSDNa9kBWaU1Soah68hyuL4TPmMdjdZVbgF/0+M2h/89A6bFzbh6npOLK5HNKZLHKqipCox1YZbbJKn2lp3FctQTPYFzVFmjVR4IwdW01LoNUCNTUdRzKdsRXjNa6/PswjKacrzlE9NFrPr5q1rJH3s57vylJ8n4jOh4QaQRBLRqs6AZTS6GLaKLVcWtUWTAC2MhK8x4M1PR4kUxkze3D00DgCPsF2DqOUhFOXAGN7razPXXv3IxTsQn80XAz2X2gQn0xn7DFpPI/eaAh+wQvW7QYYfbzpjARFzYNj3eBYt24VNIoEa0CazZr3Y1CPiK0lYEoTBaCVF+a1JlpYCxeLfh8G+6LwuWRE+npt111qrO9jsxbker4rS/V9IjobEmoEQTREI9aClZp5VssCVG3BFLv8thZFRg2yrJzFrr0vmueoVhfLSqWFX8lnHLM+Z+JJvPDSEXg41rRSpTNZHB6fMjNLBS+P/jVhU4wBgJrPQ1HyYN1uxJMpaAXNTCzgPRzELh/8gtcWG1gp0aGW1cewOA0N9pn3PTYZw7bMkM1FmlNU3ZXrtRfmdUq0MEqaSImpitddDhZj8arnu7JSv0/E4iChRhBE3TQTH9NsxmW7MYTUYF8UAMzswVqtqCq1NlJVFcdm5sruu5Zl0LGf5aRexqJ0bNaxj03Gyj432j8ZGZJdfgFGawA1X0A6k0VWdkMraLbMWsbFmOIsOb/QWaBSjbHBvqjuRi12JTAwrD5GHTzDbWkkDex54QA2D61D/xrdEjg3n4ZUrN4PBuZ8OyVaOBX8XU5r02IsXvV8V1by94loHhJqBEHURbPWguWIKVsqrLXNouGg2foHqN6K6lR1BF1+n+l6TEvZMjFVD04Lv9vlKhtbJfeiVURbC6AyLgZe3gPBy4N1u81CsZKURTqT1UWaphfvVxUVWkEv42/EpElZuWKNMUOEWUt8GLF5htt124lDttIdYkAvgGuIyx1bRxAKdkEraFjXHwUYgGNZ05o3FYtXTLSolrBQL4t9Txdr8arnu7KSv09Ec5BQIwiiLhZrLWh0QWFZt809ttw4tf4xekQ6taIa7Isip6gAw8Dn9SKZzmDP8wcqFrlt1h0Gprw9UK0m68a5jJg0j4eDl/eYMWz5QgFdAR+eGz2MtJRFfzSCydiscTlMHJu1WchKa4yZjcxLSnwIXh6Hx/UyGWfv3IZIULTFzvkFLwb7ouY7EptNmDXgBMGLuWQKuZwKv89rtlo6fHTKlmhhzKkk2y2cjVibWpGd3AqLVz3flaWO0SQ6CxJqBEE4UhrEXomliI/ZvmW4rqDwVmTbOeHU+sdo9QOUt6KyijtVzQOaBtbtRsAvmPfVSJC908LPWfpUGlRrsm4s7JIsm9asXE63muUUBflCAW6XC2q+gGg4iLUeDvOphZp1gsCb1zDuvVSAGPMlCDxkWUGuaIk7PD5lFvjdONgHwaufK6eoSGck2z1YxR7PcVAFXaBNHJtFTtH/PZvQY9oMEW+1LAJAOqNh9NDRhjMujWbvhsu22fg2sngRrYaEGkEQFakkKiRZ1guSFstIlNYHawXmYl0jKLx0fFa3pDHexWT8WQWo4OXBeziwLGuL3RIEHmKX3xyb6PdBEHj4BS9UVYXR/7s/GikrcmvcVzUrGGCPPzMsdzuGo2XjrdRkXfDy2LF1xLT6jU9OI9wtgvdwYBgGoe5AsY+nC1k5BwDoFv3o8vsgeHmoqgqOZaGoKmYT8+b5Dbdjaaskw1pnYLh8jWeaTGWQU1R4OD27U2bdmEumzXu0imPrPOsN3PV/bx5ah42DfWYdPWtHBwBwMUzDAmnH1hH0r1moMWa4bJuNbyOLF9FKSKgRBFFGpXi0bZuHkExnICuKmTF4ZPyYKQRaVQahHhdrmVtSKLolLe65xWb8GdYsa6kNQIMY8OlB7tGQWT7CiBEbm4xV7C8p55SyIrfGuKtZwUrFqDEu83hL5mNpk/XenhAG+6PQNCAr5zATn8PBo5NmjBkAeDgWkZAItRiIr6h5sMUsUL0WG4uAX8B8WjItTb09oTLLmvnsSy19xZ+NZypJMo7NxNHdFQDrdmEumcaeFw7YxJ6B4ULV93UD0JCVlYWSIcXOB9akBoNGBFYkJJoWQ4NuUU8IOTA2Udc5CGIpIaFGEEQZpWJJ8PLw+7yQc4ppVTEWS0lq3k1UiXpcrGVuyaI4smYCGvstZkxjkzGsX9ur33exsGoo2AVB4JFTVLNHJaALrLHJGCZiM2YwPbAQgF9a5FYQePQERaSKfTStGPcXDQdNQSIrimmBg6S3aULRymR0ZjCEneDlsXGwDzzPIZ8vQPB60OXXxWZsNgGe94DnOCTTGcRmExADfsg5BbyHA8e69SK5+YJZOFdVVT2BwMujW/SD41jMaEmbi9CwbBnWR0PYGS5AA6M3JwD84am9tlizUlfvVCwOD8ehyy9AzRfg5Tm43W7IuRwiwYUepKZb2sNBTsZspUJquSBFv68krk4vuKuqeQwN9ju23lpKyHVKWCGhRhBEGaVuv0hIBMu6ISuKrfm1NV6rVWUQjMU6sFBcvyweqlTMGW6yUtdfvfFzTgujsYgb92i49qzuOyPrE9ATCcYnp9ET6kaouwtpKYt4Yr6syK1xHkXNIyQGys5j9L8sdSUqqor5lISJwwlTwFkx4qPOOm0bGBeDfNFS5na5wHp59K+JwO/TrzufygAaMDUdx9R0HOvX9qIr4IPfJyCRTGF6ds7srDBxTE8q6F8TRpffB4CBh2NtLkJzrovi0fjbmNPYbMKW8ZnOZBHwWavB2e/B6EIgeHmz1hvghtjlh5f3mGNgWTfCwS49MSKfR2xCz4gtjV1zsvoa4zZaZ3l5D+ZzCiaKiRTLXYutlS3XiOMDEmoEQZRR6vZjWdZsQWS1iFjjiBaTVFAqlHbvG8WO4SjGHYLCSy0vkiRjMmbPSqw3267awmgTrMXYM0AXGZ7uAPyC1ywl0RXwmdmKhgjTChokWTbPNzYZ0xMLtIUsynUDaxAJiqaFzhh3UAzYRBoAdPl9SGWyYDm22JhcZ8fWETz0yBPm3GSzWeTzeoIAwzBgXLpq4jg3WFb/b98aNC/JMnpCIrr8AtwuF4JiADlFwVQsjvliBwLBy4Nl2WJLKj34znA7Gs/IV3RBA3rWbnJ+oZVTKiPpXQ0yC10NnESQEeM1NNgHKSsjncnaiggXCgVzDKyb1e9J0wAwgAasX9sLaPYYymrXMt4lraAhK+eQlrJlXQ+WQ6hRiyiiEiTUCIKoSKnbTwzoPSCTqQzSmSzAwDEDsBGchJKq5nFgzLn2WCt6LNZTRd9YxA3rVTqTRXxuHh6OxZqekGnJ4T0eADCtPxzrhpxTIPC8WTg3Gg7qAqwoOsQuHzhWr2PmF7wYn5o2RV2hWIDWKlDmUxl4OBZuI7K+iGH1NO75pSOT2HbiMNxul9nAXdM0pDOyKXAMN7Hg1dtIcSyLrJxDVs7pcWoaMJNIYvTQPFxulx5jx8AUogZSVjbnPiPJmDg2i3X9UfAeD8QuRrfuAfAU48msxwHVRZBp7Sq6VPVaabqY1QoaGBeD/qgHKMbhAYDbxUD0+8oK7la7lrW48fq1vRULGS8H1CKKqAQJNYIgKlLq9jPKNMzEE3j0yT3mPrVEUTXxVKtnZi1Ks+sazbarZ2G0LeIDvebin0xl0C0GMDevJwL4hbwZS1UqhqxuOMMK2S0GAGhmPTFFUTGwpgfbtwxjbFKPs6oU8+UTeIBhigKxgLlkyowFM8Y8emgco4eOYrA/Cp/XC5+gB9tPxGbMhuqGm9jqyjZQ1Tz8Pi+G1w+YiQ6SLJvvgzVubtfe/ba57AmJ6Aro//ZwLNb3r4GiqohbEiasCQDVRJBVKBuCUFEXYgODYsBMhLDBlLvBgeqCy/rutKvyP7WIIipBQo0giIpUWhxKi5xWWsCswqxWnFA1oQTkHMfWqmDrehfGSos47+EwN5/Sy0R4iyU5zAB8veQFU2L5AhayGSNBsXge3RK3pscDD52EjWwAACAASURBVMci1B1A9HDQVrzVEEux2QQCfgELOYoLaZalY77noUcxvGEAO7aOIBwUAWgIiQFwLItEUdwBKCY/iDYrmZ75ydhLkfA8JFnW/y4KNquIMfpyGiLNwOPhoAFms3WWZaGqKngPZxbCtVLJDe70Tsk5xSKUF8Z/cGwSqbRUl+Cqdb3ltGRRiyiiEiTUCIKoSDOLhtWNWanGVWm8TTWhFBDL/3uKhETs2DriXB6iQeq5x9KWTNZA96HBfgCwxVFxLI8uv4B8voD+NXr9r11799uuMRWLI6eoCAheCIIXgFYM0teFzKYNA/B6OEzEZk2XnmG52rF1BEo6ZW73+7ymqCvt5JBIpsw/Vsvc3hcP2tovbd8ybHNpKkoemayeURkUA2bG6/jktJnoUKk4LwC43S64XAwKBQ05RYWcU4oFfxesh8b9WDM+AWc3uFUol7q4zUbzRSufJOfw+70Hyp5dpff27J3bzLqARs/S0ustN1QwlyiFhBpBEI40smiUujHrqXFVTSgNiAvB8kCxj+RAr1mY1Oj7WCnYupGFrto9VhMOAMwsTkCPo3K5GIgBP8IhEV4PBzVfQFAM4KTh9WX3OT41jf5oBILgLdYJ06v1+4qCSs3n0R8NYyaRtGXWAnr/zYnYrOl+FHjebLhuHafVYmmtn2aINONzaxN3o4vCts1DxXZPuis3LWXNMiCV5nT7luGiy1GFh+OQLxSQzkhgWRbZrGyKNFVVkc5kbbXjjGe2eWgd/D6vGQdYK9nA+LdVPIc8eVuModPzP3vnNpw8stH8OZ3JmuNotziigrmEFRJqBEFUpd5Fo9SNabjNSmublda4GpuMYWwyVlVYGSLQGk9l9H2UJHt8liHoxKIL7uDRSTw3erhhC0U9GXilIk/0+7DtxE2AppkWL0DvTPDL0V3mfQ709UDgeTOOSs3nMZ/W2ymFxAAKmgaXywW3243urgCSqQUrloEp3gI+eHmPrabb+gG99VaqpEWTwUBfD4YrdEMY7Isi3C1iaF0/wsEuFAoFyDml2O5pod5bpSQOo/XT3HwKqqqCZVlbhmel+mrWZ/HG15yOwf6FjgvzqW68cGCs7l6yhmVNSkxhx9ZBswBxpec+vGEAmzcOmm5YYCFujgL3iU6j7UKNYZiDAOYB5AGomqbtZBgmDOB2ABsBHATwDk3T4k7nIAiicRbjXql0bKkb04jFsgZ1G9ayRmtFGSJQzilmyyM1XzDruFnF37bNQ1jTEzJjotYPrMHmoXU4Mn6s7FqmK9Vi9atkjSodS7UEhkrB+bKiQPT7cGBsEgBMkSRlZcwlU2Ztsy6/ADmnwOvV49aMWm390TD27j9oazy+bmCNnryg5gFGd1FOHps1s3N5D4dEMlXWWsuIM7MSDQcxvGEA2zYPoX9NBF0BH9wuF1Cc53xWhodjsWPrSNnxsdmErQyH0dqJ5zjsPziGsckYzjptm2n9M+ZZdx3rrtqgGCgmVyzQFfAh1N1VVyC9UycNawan8Vy3bxnGyMZBCIJXd1EXCsjlFP198nAUuE90HG0XakVep2natOXnGwE8rGnaTQzD3Fj8+Yb2DI0gjj+qCaVaAq6aO7DUvbfn+QNlVo1makUZi6cY8IH3cKYIk7Iy9h9cSG4Y7Iuiu1hA1uVy6YVeWTeCYgDT8TlbFwWjFEN/NGxaViaOzZqfN5OBNxNPlncmKNbkMu+hRAAamZ0z8QQkWcHWkQ3oXxOB26XHerkYF/w+AVtHNpoZl+l8Wo8dy+Xg83nh5T1QFBUCz8PtdiGdkUyLZkaSzd6cVquf1boFAJvW9aFbDID3cHCZtdcYCF4PeA+LLr8PXQE/3G4Xjs3EzQK90XCwzHJnLW9x0vB6iH6fWZpDUVXkcqotzjAoBqCqqllI2EDTtKasudZOGsY1DDEaDQch5xSoqgqXywUv7wHHulEoaJimwH2iA+kUoVbKJQDOKf77VgC/Agk1YoXTKQHC1YRSrSzNWiKr1BUIlJfwaKZW1Ew8CUmWi/FLEmTWDUXNY3p2zta0HNB7VHIcqwsdhoHLrS/G1i4Kxn3qcXSCJSNRbxJuWL+aycB75HG9dEl/NGIG4ZdmR5YiZReyaSPFDEwx4Afr5qCoedOqpve+9OPFuWPFdkq6GAUAl4uBh3PD7XYjoeZtYqmQL5jWvJOG11dsQM4wLvi8vC7QGOgFZBkGDBi43W6oeRmABg/Hmu5Y4xqFfME2V0YfVEMIpzNZTBybLXY28EP16uU/jDhDhmGKrlIJMsvC5+XhcrkwNVOfI6V0Tg2rJuNiioK22Ke02G9VyspQ1DwKhQJyigpFyWMmkcRsYr4jYtQIwkonCDUNwAMMw2gA/n9N024G0Ktp2gQAaJo2wTDMmraOkCAWSSUrVCGzNN78WoLQSSiVijSg3NJVj8gyXIFOlrdGLVXG/aTSki2AvlLrqrHJGOScYooXDbpVBtDM6vxWGBdjWt9cDAPe44Hfl4er2OOy2Qy8Rx7f43hcJcujJMvm3B4Ym8C6/ijyhQLiyRTYYhslb7EzAOt2QQPgYlzgORcKmgZF0a1RieQ8BK9Xbw9VYW4jIRECz5t9LQE9NisU7EI2mwMYgGNZMGBQ0DQwmoaCBuTVPKSsDDWvJwSwbpdN+CbTGRwYmzTFvuFKDooBsKwbkZBoKVWi6a5rdSHO0Cgg7Pd50R3wwePhkMsp2DK8HiExgHseerTqfJfOqe4id5s14wBdkP7hqQmz3+p8KgPB6wHrdmPi2Czic3qMH8WoEZ0Go/8n1sYBMMyApmnjRTH2IIDrANyjaVrQsk9c07RQhWPfB+B9ABCJ9Jz2pa9+fbmGbUPg3ZDkfO0dVyE0N7qVxufly7arSg4ZWW3ptQSBNyvRA4CSz5dVWXcaj5LP2441sDZidzo2Y8nqq7UfANNiUigUHMcp8G7AxZpjcrlccLlcZvC3q9geKZPNQpYX4uDEYisnF8OYVca0YqmIfD4PJZ+HUsyudLvd4Hnd1QcABU1DIV/A3Hy6YsHUVsKybrhdLvA8B7fLDU3TdIGo6dYx1q1vK2ha8V70u9E0QM5KEHw+vT1UcZuaV6GqBb3TQaGgV+5nGCiqilQxUYH3cKa1yZg/l0s/h5ovwOVyFYUrA02Dfs3iJOYLBaCY5GCIw0KhUPbsrNfweDgzo9U4V8FYc4p/q/kC8vk8MlkZXt4Dv8+rX7uwUMg2mc7YnrF1/vKFgvnusawbHtaFvAb4fYKtg0Ne05CcT4Pj9HfK5XKBY93IFzTznQLK3+XjCfr/uDrLPT9XXXHZE5qm7ay1X9stapqmjRf/PsYwzI8BnA5gimGY/qI1rR/AMYdjbwZwMwD0D27Qnjk0u1zDtnHKhjDade1Oh+ZGr20V6est2544NtbSuYmEROwYHLJtEwCMFksqWKlk7RqbitlKPBg8V3K8mVXZ5QM0Paty17N7SrIfPRXv2dqC24hR2lVhfACwYziKSHTAtq03GkJyPgOxS6/5Zbjt7DF2Ks46dZuZ9Wn0Jo2NT2FsMm7LDt28cR02resvisY85tNZqKqKhx99EqOHpsrGZKUVrmxriQijn2o6IyE+l0I0EgTrdmF2bh4Cz0Pw8lDzeaiqihef34tNI1vAsiwY6OIipyjmnHg8HDjWjYnYLCRJRkZLWBq2D5tWSTHgKyvBkZzPYN2A3k1gMjYL0e9Dt+g3xUtayuLg2CTG49OO3SZ2bB2E4OXRvyZsupalbA6C14NjM3HkcqoZszYRm8Xho1PYPTqGs07dik0jm8rmac/zL+HxF/aaP2/fMoyIg4v+lA1hpPIeBKMRWwcFSZKRmM7iwOiE+ewG+nog+Hhw1vOMjjX1LFcC9P9xdTp1ftoq1BiG8QNwaZo2X/z3+QD+EcA9AK4GcFPx77vbN0qCWBxOLr18oULrm0VQzaVZKiicXHr1xmT1hLvNdkkb0YdIUCzLLARgWyhR7JltbUlVDcN9aWUqFocky3p23nzGDIQv7c95eHyqZlap8XOwKwCOcy8IkUwWhUptiSw0mrVaieENAxixlIhg3S54+YV+onPJFNb0hBDu7kJWzmE+nUEupyCZykCWc2ZT91179yMoBnDGjq1IZ7LIqaqtp6Z1fox3we/zmsIwMTcPrhij5xf0Xq4vvHTEloAA6O8RoLuXrbXLAFR07Y5sHCzei4SEmsd8KoOugA/zKckswAsAh8enzDhDSVbM1lhWK9fUTML8txEnaX23rM+fZd0QfX7zFwHre2bci/GeGO7aTogdJQgn2m1R6wXw42LsAgvge5qm/YxhmD8BuINhmGsBHAZwWRvHSBCLwqmoa6HF7pVKgrA3GqpYesIYV+nCVCsmKxISsX5tLzjWbdYJ6xYD6Bb9ODIRMxdFgecRCnbZYoQyUhaTsfK4PKeYoEpC1ljcazXcrje2bGwypi/6JTW+qmV2NpO1WopRIkIM+PWSHIoeVyfwPDiOQz5fwHw6Y7ZIsgbuHxibQMiTx6NP7jGvt2PriBlzFuE9cLvdSGekigkU9gbnGqYTSVtWJs9xOHx0qqxrQD2FgA127xtFKiNhx9YRWzxhIpkyBaBRSy4aDiIaDpplRNR8Hl1+X7F2m4TJ2KxtLKLfh95oCN1dAdPFmkim9N6mfVH4XDKEYBCi3wcx4DOzU51+6aDiskSn01ahpmnaSwC2V9g+A+ANyz8iglgaKgmHUzaEax/YAKWCUBB4QINN0DQqKEoxFj/D6gH8P/beNTaOdE0Pe766V3V39Y1NNqkWJQ5HmiMNj7WaM1mvj4KFd3EAI5vNyY84SLLJwkic7I/8MeIYCfzH9g/7RwwE3gUc2FggCBwgyAESIMna2STI+IJF5uyufebIA2s1c6TDocSheFGL3c2+Vdc9P776Plb1hWyS0pAjfQ8gaNjsqvqqqjX19PO+7/PQfrMwCjOkwDR1xFGMvZctToDY6+NK2ixSFARhdpJwoUynEQn4JGE6nuqkfM5ZSF+zNJk9abtGvZaZJExfm3muKyN6hbwF09BAJEJd9SUJhACEENgFC6ah4uVhhxMNhiikJrTsWOs3VrC0UIaiUFUwCEOYhg5XUTJZnQyMlA6GI2iqAl1VM+Hv06Kdpq0/jWmfq83nu5nkBoBe283nu6iW7YzhrmnqqNcq2HvZwpOvdlAuFZAzDXz+xSYe/snTzLEkWcJitYycZXDVNWcZ+FN31jEYjuB0aMmanRMzvhVkTODbistW1AQE3hl8E9/c04TQLuQmHqjAyYTiNKVkpb6AYiEP09B5uSwMI6iQUchbPBZIV7MeXVytGiNpp5Eidj6Nei1D8gbOiDvJA1kyetZS1lkmO+/dWcfqtSXuk5Ymi/Mapdo5OuygKjI8P4AkEUBRQAiB59MUAIkQ+EEIz5scNpFkCbqmolq28Z31VdxOzFt1TYVlSPB8P2mwDzJmrzv7TWzcXsuURRVZ5mTOGbnY3p1U0qatf9br8yq07Bqw0qWuUmWMpVi0Oz20Oz10jo7TFtZvrGCpWkI+Z2VsSRgWF8rYb7bgHFdJqTraGwiSJvCthiBqAgJvGRghnKZ8ACfbYJyklDBrh6NuH4WcCVVRECdRSY7jQlVkXmbdax7C1HUsLZQzxOBPnj47c5zTYZuW5tIkj7vfayonGvfv3ppw4Z+3d+wkEp3OkWQxSczegpHF7d2DuclAdzDkxGSQGMWqiooYVEWMoghR8t/pe2UaOooFC6aho7W/jR/+4D5KdgGu56OQM+nkKiEIowhDx8WznX1sPn+RMRrGmEPJUX+Ax0+zAe3zrP8sr49buxy2u1ipL2C5dqwo+0kbQHrS1jR12IUcqmUbD763gXry/pxlwtA1eL4PiUiI4ghRFCPwQ35d51mXgMC3BYKoCQi8hWDkYlrcz6yH8WlKCf89ATzfp4paTJ3vv957iYVyEYau4PHPn2Hz+S4efLyBop2DIssIwhBHvQFfCzNfnReSLNFyY9LvZJo67DztY0qXW+u1CtrdPuIonmgyPyt4vFSi5JXsPHRdxUGznYlJ2t49mCCDJyl04+kFrudBliQYhnZsXQGgN3Dw+Okz5C0TN64tQdc1WKYByzTQb+2hkLOgqQpcz0cYRjBzJoIwhJxYmOi6NqFisXWnJ2LTZrjznMOsnsv0e9Lbjvvzsc/kYDjiJF5VZLS7fa6MMsPcWqWE22vX0ViucVLLiGlMJO7r5vkBXrWP0Do6XsO0MvtJYMotAFEqFbhSEERNQOAK4HVOno2XLx3Xxe7+dCuFNE5TSrqDIUxTR840EEYx4oh6fFmGjg/eu06b4Q0Nv/QLd5G3zISUMQmHcD+usxqKsvPRNRWVUgGqosBnQdomzcPs9odYKNmwCzkYusYHHQbO6FwGpsyChDn4s9ijtCM/+zOejDDPRGgmvcCjNhlFOweAQJEl9AYODttHWGsswzR0riYxSCnzXkWm/nJAYlZrALIsQVFoNucnn34GILl/yb7UpJ8tZxpodboTRG3WObDP6c5+c2bgOdvWNCgh1DSV56ymzzndF+d6Ph797CtO7NIDMDnLoIQ0mY4NgoAH2IdhiCCMcNTtc8J8f71GbWCSz9v9u7dOVVbv3VnPlIU3nDU8+tnWmSd5BQTeBARRExC4ZLwOqweGaeVLU9fnIoCnKSWH7S4cx+W+WEQiUEliGhpG3Cg0Zxm4vXYdIEgerHRfLHR7a2dv6rqnPfTT53Pwqo1yqYDlWgUvD2kv3PJiBXYhh2IhD0WW6eRjDE7UcqbBUwbmBTsmmyhk59sbONA1Fcu1Cr7a3stcn/HyaBqzVL3x9IKSncd71+sYjjwMHRfrqyuIY9q3xaw0wjDCyHWZVyw8PwBAIMvHxI3lV0qShOsrNX7sRr2GhUoRlWKBb/vyVRumrmfWx2xD0j2GtUoJDz7eQKVk876y7RcHnLyxcHX2XlbyNnSN9xEysub6Pu9FY38A8Htv56xMz+FgOAIAnmYAUBXy589eYOCM0B84UxWweYdoqmUbqytLmRJ9zjSwem1JKGsCVwKCqAkIXCJeh9VDGufJ0UzjtMb6rZ093H6vgTAM0RsMoWsqCpaF4cjlpSmAqiD9gZPq5aJkxw8C3L11E2uNZW50exJRHT+fOKI9ceUiJX2apiJn0uk/Z+TC83zIsgRD1yHLBK7rI29Rm91p5zWr0R2gJTZD12AZOqI4gpKEnbe7/cwk4YOPN3iup52zYJkGbWqfMhE6frzxuK04Bm5eq2dIg6FpdIIXAFSqIBJCySgjMYCNKIpgpMrcURRCVRRezqtVStzLTFMUhFHEzYDZ+u7dWcfGB2vcBPeo2+fK13ury5l7Yect5HNmprQOHAeiA+ClyULOzPiatTrdmSX5cWW3fdRDr18EkpSBnGXC83xEUQxT19EfOJnP6TT/vfQ5TnudkfI0dFUVcVICVwKCqAkIXCIuSqzGcdZGb2CSrJzUWB+FEY66A26YChC4vo8wzHrCDYYjuL6PTrePcqkAQ9fQ83wEQcCbyE1DR+uoO/GgZ0R12rpdn2Y4AgRBEMDzfD492er0MHI92IUc7cEigKFr+GjjNm5cW5oYMmDHYuW3bn+Ap1s7XIFbKNvIWxZUlQ5NRAYliSPX45OE6WSBnGXyaURVVTjJYedxUjkxXSo8LoHKkGUCQ9fgByGPS2K9gXvNFlqdLvoDB6vXlmDnLNxs1Pn7eoMRPxb7nBXyFkxdo9df1lBfrGD/ZQt2IYf1GyvY+GCNT/UCSK4LTYLgxrxJ3igjhWn7ENPUM5/pIAjh+QGCMOL2LeNl1Hl64D797BH6QwfvXa+jVLTR7hxPg45/sZllJH3Sv41pcWGu74tBBIErAUHUBAQuEechVifhtMDveaKkTnqIdgdDHLxq4/pKDYauwfVoiRGpTMXBcIQnW18DoA9RLbHxCEKq8DDYBQvVso2BM8o8eAFGLLyJ83EcardgmUyxiTByfQyGDkauBzXJGJUkiWZnEoLlxSqqJRvPXxzw4O3Va0tATFWhnHWs+F2r1/D17ku8d2MFtXIRiiJDIgQRaElRUWQs1ypodbroDoZYrlUBJBmTzK4koupbzjJQLhbQPuphdWUJ66srE+VEdp2XFsoo2nlYzPYkyfhUZBmKIiOKIrSPejB0DUPHhR/QfE1T1/Hl5jYA4KONWyASoX9AoGsqjrp93kOXtgQxdBUSkVAt2fye2HkLi9UyBkMHnh9AUxVoqgI7b6HbG2aUUQDJkAgNg8+bBvrsPsbIKIIvD9vo9oY8gSBdSp/1hWDWZzAKI6zfIBPvT3+xGfffA04eomFJFuyzANDexu0X80/yCgi8SQiiJiBwiZhngu6sYA+576yv4ua1Ojw/4KpVNhNzetn1wccbE2WpdJqB47pQFYX3gR112+j2h2gddSf6hR58vJE0dVNTVxCg2xsgZ5mJMkYJAhsIYP1P3cEQeVvJnA97aAPA97+3wfenqQpMg/qIgVCrB4lESUO9DE1TYWgq1laXoe0pOHjVhq7S4HCqDB6TrELORLlUwGK1xAkMkQgUSHDhQZFlHHXp9GqjXoPr+VAUBZah8ZB5z/Ox12yhbOehaQqWamXcvXWDpwWkvddYX9viQpmHoeuaCkkieNXqAgQoWCYc10+VOYE4NR3KmvtXV5agKkqidMUIwhDPXuzze5GdgCRc+YvjCMuLFSiyzJv2B0MHbqKcPXuxjy83t/HDHzzg1wmgilPZLqBYyCOKIiwC6FdK+NE/+if4zvoqLwenVbSzYBqRm/eLzVm88dj7d/abYupT4EriRKJGCFmP41iMvQgIvEGc9aEyDx58bwON5UUUcrQ/q9cv4snWTqZMNK3sapo6SnaeG9cCk6Wl3f1XqBTtTOQSez09Pch810DoFKKaKDSyJNFyWOKd5Yw8LFZpJFAQBBgMR2jUa4iGxyW18Yc2wbFqk7NMhElKgqnriKIIkCSokgRC6LRpDECWCIo2ndp0fWrxYOga5NSwQRBGqFVKUGRKIqMoAiBBlggIIej1Hd7XBVCSqWsqP7cwivDysMNJrOcHKNt5BGGUpAXI3HuNRVUxckCPFyckjEBOeuLCIORTrgBVe6JUeY/tQ9dU7L2kgdILZTspTR+Xtrd29lAu0jL0YDhCIWeCSASSJHPSzNTAIKCDIEfdEb7c3MZhu4uvd1/CNDRutxIEERYXSpAigK1G01SU7PzEoMRpHnVn8dSb94vNWQ2mRZSUwFXFaYrap4SQX4vj+KffyGoEBN5RvM6HxPqNFdRrFSgpAlLIW7wMx8pE09QJligwjnSwe3cwzEzrMYzvj7nP50yDKjSeh7xlAYh5yXQwHKHbH8I0aEnvsN2FM3JRq5Rw6M1+uA8dF3vNFuy8xSciaW8XoKoKJEKJFQBEcQTP8xBFMZTE1d/zfYAQmIYOSSKJ2jVKerAoaYnjGIQQSpwILX2qqozlxQotPbouNE3l51bImQijGK/aR9BVGtEUR1T5CgJaIlRkaouhayo3yW3UqUdYaOjQFCUZ0tAwGDrYa7a4b9z2i4OJ5v1mq4NGvZZJS7DzOU4+/8xHH+Led9bxZGuH3l+NKqFG0qdGCCWELFKq2xtwHzoikUxJ+uHjp5k0gWrJhu8HcEYemIIXBCGWqiVsPt899TN93mnnN/HFRkDgKuM0opYD8E8JIX8+juP/95tYkICAwMWwVKUPP5bFyZCzDLSPepxQTVMnWKJAZn8L5Yx5aLPVmUvVYA78rPk8CCN0uj0MRy4UWeakrGTnEQQhDjvdDPmTJWmi5MmisQBaytNVFSjQ8mcYhnwSUpYlqApVuUauh/ZRD4qiwBm58IMAhbyFV+0jAMlEokHLhX4QcILHiBpAY7K6vWFyHalKefNaHaoiww9CtDo9fL3XBGLgsN3BwWGHeqAl05qKQtfXHzqIoxib27uclOzsN/FA2eBN/jIk+EHASRoAboUBUKK6tmDiy8c0A/P+3Vv8mtmFXBJo7sP1fKiKgnKxgHqtgv1mC0e9IVw/QK1SgixLtNQqqzTVAAT//PMv8OXmNjX6TQYK0j5k2y8O+H0f6CN4foCRmyXsB4cdnIaLTjsL9UvgXcJpRO3PAvh9AP+IEPKfxHH8P735JQkICFwEB4cdbOBYxWF9RYPhaIJQTVMn0kqHadDSZbq/qVYp4eHjpzMNT9P7IxKh8UYSgUQk9PpDfLW9l0lMcD0fA2c04SKvqgonIcypnllF2AXqsu/6PlcOmRWE6/lQZert5vsBZFnilg6mruHGtSWYhk59xA7b6A3o8XoD2kSvKiqOugNYpgaAgEg0feGwcwQtURyDVCmS7sun/VgjFz/b2sFhu8sDyVVFQT6JeDINHb3+ENWSjQcfb2B3/xUkWcJRly6Cpzh0Z0c7Hba7WLEVHLa7WGvUsVQr80Z/y6QKISF0WpRZVdRrZcRxjINX7WTugw4rhGGEOPl76Iz4YAIAgICnQTASlfm8PB5mop0AYL/ZOjUrFHj9084CAm8zTiRqcRx/Rgh5AOD/AfA/EkLqcRz/t9/M0gQEBM6Dzee7+PDWTdRrFd4UftTt45/84U/n6uWZFuzOLCxYKbBRr+HzLzZnTpEymwYtMTYt5CxEcQTT1FEuFfDJ//nZqTFDUqJmsfIpAN7bZectrvL1Bg7kpKSYs0zIkgRZltAbDOGMPHieD01T4fsBLFPnYQmaqqBaLiIIqBL3qnWE5cUKysU8nJEL1wsQRiFcL6BTnKaR9LTJnAQvJqau7Pf7zRa/Jp9/sYn1Gyso2Xkc9QeoFAu0PBiGuL5cg6oq3EAWAL7ebc4V7ZSGlBxXSdTDMKCTtQSALB+XcD0/4L1xz18coJCzkj48Alq2jDJ9i4z8MaQTHtKfl9/75Mc8LN1xfXSOenOpYq972llA4G3GqVOfcRz/nBDyZwD83wD+NiFkJY7j//LNL01AQOC8SD9ADw47c6kcabCHcbVs82gdZs3g+QEPyZQjRQAAIABJREFUQk/3FLFyFnvIG7qGnGXAD0K0u32qfBGCvGlg/cYK72Nix0sTNztnYaWY2EbkrKSninAScPCqjWarg25vgIePn+I766s0DQG0IT6MIgRBCFWRac+YpyKfo5OmiiwjjCLIkgRNoVYYR90RQGiJUlUVrmypqgI5KdOqisyHAkJdR62qQEtIVhCE2HtJTW7Xb6xwJSwKI3S6fZSQx8igfXmKovCYK9bvVSkVoGkq1KQ/LmcZaB11J4Yz0mVggNpVDIYj7jsXhBF8LzjurQPgeT4fbnBGLp8QTVtoAMe+YSU7z8kfK1mflPCw+XyXq4fVEl3Haf1mb2LaWUDgbcVc9hxxHL8khPwygP8dwH9BCKkD+AtxHAenbCogIHBJ2Hy+e2aCNhUJgUlbM7DA7DQpSQ8PALQUKREJuiph6LiQE/uHIAhx/+4t5C0z8zBPKzUlOw9ZlnF9uQbTNGAXcpRYaXQdg+GIJxsAQH/gwPOOjXeZmgTgmAypNgo5i5dh/ZD2xfWHDtqdHkp2HiwgMoppf58sSVB1HV6OTpZ6QYDeYEj9zRLiMnJ9Xna9vrKI68s19B06SNDtDxAlAfEMlPwkZdrEvsIPAhRyViajNB3tNN543z2k95X52nlBgEZ9AQDQGwwxGnmolArYf9XGUW/ArwG7Zif5htmJ2sYmhgGglyh803DefjMxFCAgMB/m9lGL47hPCPk3APzPAP59AP86IeSPAfwk+fNZHMdHb2aZAgIClwE7Z3HneaauBEEAXVNh562MlYfjuryMB1CVyfV8qCqdymRqXBAEcD1/4mHOHtor9QWYuo5w2MLiQpk7zYdRBFVRuErHwIhCtz/MWHYYhg7EdHqx1enCzluolgpcBSMSwWDo4MlXX6NWKYFIBJahY+TSrM1CzoCmKZAlGUtGBXEcIwhCDB0XR70++kOHW4oAwPWVGoqFHGIAdVACx+xLXrWPeJxWb+BAVeRMX16v76CfTIky8sauP4AJIqTKMr92jutirbAMVVWhyjJkiXq9Pdna4WkMzMssXZad5RtWKhagKDIf7GDl2lmK2kX6zWYNBQgCJyBwjLmJGiGkAuAvAfgV0MaG68mffyf1nq8A/Is4jn/jNa9TQEDgEsDKbN3+MNOzRAhBzjIyZThT19HtD7hNBADsvTzkJT03iSAaDEecBKQzJlkvHLO/ePb0EI7rQVMUdHtDaJqSEEHalP8rv3Qf//SPHqJRr9Gmd4+awjKyJksE/aGL0chL1jbEUX/Icx3dJC9yZ7+JfM5EKaIea+ViAZahQ1EUEJDMOcuyBFmmdh7MT42VCYsFi/aHJb11uqZRQ1yZTnGORh4eP32OzlEPK/UFVIo2X/e0aVt2/ceJkGnq8HoyGvUaGvUaKiUbRTsHNSnXej7tyfv0Dx7xazxr4GPc2PXenXWsr65w9TOMIsihDMDjmalpVMs27EKO9w5O++ycFee17ZhYlyB6Am8JTiVqhJAVAH8FwH8GatfRBvDXAfwIwIcAvgfg4+TvdQDvARBETUDgLUC6l4gpQoPhCHEcT53UfLq1g4Ezoq70iZrUbHXQHzr4pft3oSkKdetfKKPbp55s6dIZTQugvXDbX8kwdY2ShSRDMwhp5mUhZ0KRZfx7v/4rfHIRoJOt7aM+DF3DXrPFfcBYjmYQBJmJTdfz0ajXYOo6Ot0+Ot0+rq+EqJYKiCI6GYk4AokJT8kKo5iqiqqKg2YbpqmjmGflQpqGwEmdJEHTVFSKBYwMD65fQxRF6A8cVJJ+rhQXRLlU4KratAij6ys1FHIWHrX2cbtxHZpG/xfOrg3AorrkqQMf1bJNrTfG7FbSmaOuTyO55EIOOdNAEITQVAUfbdwGcNyXmCZUdsGCnbd44sJ5+80uatsBUCJ7v7HGfz4P0RMQuEo4LZngdwH8JgAdlKD9bQC/Hccxc0F8Ctq3xt6/CkrYBAQEvsVIKxLpXqJSsQBTV+G4Pm8cT6M7GGJriiv9vTvrKOZzqJRtKLKMOI7R7vaxvXuAbuKPYRo6TwugzvsxwoiGeQ8jSioYaZMIQc7SIRETQeKf5oxcqqYNRzjsdCfyQwnAg8UBZJQ9dnxdU/GqdYT+wEGtWoJECFRVSZQygMS07OgHATa3d2HqKrZ29pC3TPzpX7gDTVM4UQNoBKqqyLwEqasqzxl1HBeO42KpVsZyrQLfD2CaOvwgxH6SMAAck+WPNm5jMfHIkwhBuZgHgEwZGAA31c3nTKw16pl7sLqyhOVFaqcxcEY4aLYzmaMAkp65bC4rtS2RsbqyxLND04SKEdZmqzM1fmleheuith3Vsg011Z/I1nkWoicgcNVwmqL2n4IStL8F4HdSBG0q4jjeBrB90nsEBASuNmaVnhr1Gidnlkk9u4YpRS2toqR7j6plG6srS9TdP5UYkDMNfLRxG3/wzz/H0kIZOcvgkU6yTOOfVEVBFEVwXR+DxOfMzudolJEkU8ULNDXAD2jZ79mLfZi6zolXIWdCVRXsNVtQFQWKqmA/mdBkxIJNtjIMhiN8/sXP8Qt33sfiQjmdOQ8gplmfyzU4jou1BvWJiwEMnREQA/mcCcT0NVmWoWsq7c3zfdg5C6pKfdBAjkunbBKUAADJEoyd/SY2PliDM3IRhBGiKEoioqiymfbLC8IQiiyjUrJ5OZX51rGyL7v+pqkDMfDBWiNjVNvr0+lPiRD0Bg43tdU1dSaZchwX3d5gpmXL+OdpGi5q2yH82QTeRpxG1P4a5iBoAgJvI97FPpdZpaf1GysTrw8dF1s7e1NNWdOwczQPU9c0EEJ4TqVEqBluvVbh5b8gDOH7AWIgIXRJ+RExVEVB+6jPvcZcz+cZooosQ5YkDBOFbHmxgqWFCqIogqrSWCbHcfG104Rp6NjePeDKT7VsZ8qPAAACfLm5jf1mC3/ul/81VEs2JEnigw2WZUBXVa6I5UwDfhBAVRQMRyN4QQA5eb+pa9BUBZ0ggJ2zULSpEsaIlaLIsAwNnn9ckmX7ZgTDzlkTfYJBECCOwXvl2GBD+6gPTVMyZWlWih6PB1tmZrUkS75d//i96eQB1/OzfYmpSCnHcScI1VlLmRe17egOhlgpTld6BQS+rTjN8PZvflMLERC4SngdDc3fRsxSJFgs1ThmmbKmSW53MEwe+nF225garVqGxktnuqrCGXko2XkQ0JDydID77stXcD0PjeVFBEFAG9llGbFECZ0eRXjwve/yrEtVoQkFQRBm+r/Syg+bbB0nHXbOQhRGaLaOUEhdF0WWoasqiEQydiS9voNX7S6qJRsD5wjtTg+mqWO5VoGiKPA8ajp71KNTsrnEdoTFUJmGnmSOOtzOgw9zJEST9QkyPP75M3y5uQ07Z0GSJURhxE2K03B9H7qmotPt84ELmmlKcNTrc1KXJt+tThc3G3V+vMFwxPNJAcAy9YlUgnFCdR6F6yK2HYftLvylHNJjD8KfTeDbjrmnPgUE3laMPxReR0PzVcVpD8BZygPNrpyc+pv2/mkkd3v3AAuVIk8OCKMII9fDUbePr77ex1pj+VgB6g+hKjKiKOY9ZIpC+676Awef/uQRHny8geVaFX7SOxWGMfrDIRRZQamgw0+UOT+gylW5WOClRQBodY7NZPk5xEiUPxWIj1+PE7LIFLAojuAHIeIohp2nZrxBGPHhiYE+Qj4hN3EUY69J+81GoxGMgcHPs75YgZ3PYei4SX+dyZW3cTsNZsPhuj4lrmGEP3n6DJ/+5BH/ffoej39+HcdFq9OFqes8hkvX1IwVCAMj31s7+/hyc3uqhUe1bGPouNh72aL7Sc6dGe+mSfo0nKZwXSTL03FcbD5++s6p4QJvLwRRE3inMY1UsOb2cVzVPpd5EwjmUQlZ6Wl1ZYk/gLd3DzLu8+ntpzWNj5OE1ZUltI66eLL1NfoDB/mcAc8L0O0PM/ve+GCNqze+HwAEPBgcoH1TrJH902RggU4wGnxAwDKMjG4XRXQi1NA1eL4PRaEeY2kz2cN2F5apY/3GNU7GnGQ44eHjp9hrHmJxocz32en24Xk+CnkLpqHz3FC7YMEuWDyVYXGhDM8PMBg62G+28NM/+TmfuFyuVShplSUMRyH8IMTXuy9BJIIXey95Xmj63pm6DtfzsVAu4iUh2G+2MA2zyofjShWQDXRnSJOoWYSJW6L4PvfRm7a/ZqtzKQkEIrRd4G2CIGoC7yxOIhVp+wKGq9jn8sMffJ+XnzYAfHjrJn7vkx9PvO/MKiEZ+xvzlaTGS11LC2VqWhvWMXI9DJwRnmztYHf/VWYfLNbIdVN9VDElTEhKpEf9LIE+bHfx8PHTTC4lVZvoFCgLJCeEJKkFUeaEGPGulm3EMe2/CsMQmqbC1DXcfu86TEMHITR6iRn+soGFStGGrqlwnBFUVUGxQHvPqAro8ab+9lGfD11Ypo7G8iIPqkdMe81URebq1sFhh1/HcYX3+nINhbyFnWcK/twv/wJ29l5O3O9q2Ua3N0B/6Ez0D44TmPOQKDY9yvzy2PSoadAc1fS/m1qlhIePn2Jnv3kuhetd7BMVEBiHIGoC7yymkYqcZfDyl50/duWf5wH2TT9U1m+sZHqEAKBeq/AczTTm7RVipIBZRwBnK/tmGs0NHUU7B01V0EvIV840UCnZ+HJzO7M/O2fBGbm81Fmy8xjEMUYj2pfV7Q8zzfUMh+0unu3s42ajDsTAXrOFWrlIMz0VGbqmcVWLgYWTs7WyYQeqyikwE4KnyBKPWdprtvCqdcRVxv7AgalTk9dOtw/ToAqd79PUhUqpgCAIEQQh93hr1Gs01SDJPQ3CELqmccsQXVVBAKw1lvla0wpvuVhAIZ/ulZMm7vc01fSkYPez9oOlSWMcA6oq8+nR8S826Xu7tbN/5n8Tl90nKkiiwFWBIGoC7yzGSQWzZ2DlHNOY7Qs1jst4qMxq8F+qliaI2km9QtWyzfuQZsHOWWjUa3OXTmuVEnRNhSLLPDaKQVfVCcI1vr5CzsSRJMEwdBi6Bk1V8bXzcuJ9rCTY7Q+hqypanS7+4Sc/xv0Pb+HaUhWeHyCK4ozqBlDVix3/eNiBkh9JovYgYRhxQ1ldpY344+77mf11unReYmyCdHzS0uPXgkZYDYYjuJ6Pze3dCW+6WqWEfkIyx0PUgyR7k93v8/ZWnqVMaOcs/oWGnQMAbL+gU7SnlVLnxWX3iV42SRQQSEMQNYF3FuOkAkDGbd8ZTfeFGsdlPVQODjvYmPH6OGb1LTXqNXz04S0U8haCMIQzcuH5AVcSGSRZmvscP/9iE+s3VrDWWIZhaLCMbDQSkQjsQm7qtqwnTVWpR5ipa/z1/tCZ2TTPFEBT1/Hg4w2Yuo6R69NEgsLkVOfDx08z14aFlNM4JC11jCLCMOIDAQzjpq9MUWJ+ZekUh4xfW9KHJ8sy723be9nixr/TTITp5GkH5eJxNBfNHaWEj93vb8JDTJKlDGFka2D35nX1o12mH9plk0QBgXEIoibwToOVfhr1GlavLZ2rL+11P1TmLblsPt/Fh7du8vKnoig4SmKQpmFaM/kPf/CAu90DNJ+y0+1PRAxFiXozzzmm1Yg4jqlTfhJvZBg6arKM/IcGNm6v4dkLWpZjPl8ggKEpaHf7CMMIvcGQbx9HceZhOe26l0sFNMwanZJMSql23jomUmPTlOnMy/7QwS//4p+CIssghFqDyJIEz80qYmx71j92/+4t7jxi6joc18WPf/IIkizxfExG7Nj7BkOHZ58+/vkzrohNQ3cwxNbOPvpDB+ViDoZhcC+6/WYLnW4fa436zND019lbGYXRhEXIwBnxz8dFrDXSuKjx7UUgTHMFrhoEURN455Eu/ZxHDXidD5Wzllx+75MfY/3GCu7fvQUiEbQ7Pdy/e2vmdulzvXdnHYVc1nJDUxV4Hs2Z7PYGGcuSec5x/cYKbt1sHBugJmaszcMOSnYeq/kc7LzFLTpuNupwfR9Dhzbr9wYOXrWP+MOS9XkBtISYfliOH/v6yiKqJZtbaQyGIxy8auPgVRvN1rHKyEjTvTvruL12HTnLSDJCe+j1HahKF4qi8OGBl6/aE9djHJkoKp32v6VLxezvjDVGYmnBSM5JihT7XHy1vY9ysYAgjPCPf/xT5C0T3//eBlcKCTA1LeKs5GnW+7uD4VTPuddNoF6nOndWXCZJFBCYBkHUBAQSnFcNOOtDhR1DUcKJ189Tcul0+9TQVFW5cjRvqSaYppQRTPTlzXOODz7ewN33byKfM+F6lDT4rB+rWkKxkIOqynwaU5FlSCrL0qT5jIWcBVWRJ0qNvh9A11SUigWsAfz+NFsd3H7vOq7XF2CaBlzPh2lo3PDWNGjDfz5n8jilWqUEx3Vx7zvrmeZ8Z1TFXvOQXpcgAFu66/kz+xRnqS/j/XwAeFxTemgCyBKAaZ/B8c9F+6iHMFEo05YmAFW3/uTps8y051nJ/0nvT38O0oprmvy/rt6u16XOnRWXSRIFBKbhShA1QogM4CcAXsRx/OuEkDUAPwJQAfBTAL8Zx7F3mWsUeDdwXv+leR8q6QeZ0znAvTvr/EF23pLL97+3gbVGHUEYIQgCbpdw0nZMIXNGLnRN5f5hnh/g2YwJvZPO8cHHG/jFe3dg6Co0VeWTjr2BQ0uaMS2ryqnyHElyP2WZJD2C9OfFhTKe7ezDcT20Oj1USjYKeQt2PodKqcCVsmargxvXlrBcqyBvJc78UYyR60FTFbiKAl1Tqd2Knu2Tu73WQNHOIYqOXddMQwNiZEp742784ziLyjJtKtJx3YwVB/t7fCJ2GtYayxmSBtAYqbXGMh4+fnou8+Z53j/rc/Amersuyw/tskiigMA0XAmiBuAvAfgCAKuv/DcA/k4cxz8ihPx9AH8RwN+7rMUJCMyD0x4q4w8ySZJwa7WB/tDB5vPdc5VcHny8gevLNd6Ez/IiTVOfuV2aLHoenXD1ksiiZzv73O1+2oNq2jlWyzZuXqtDUxVEUYwwiqBrKggIclZMA9YBhFGEIIgga1Q9I4SAgCBOcjwBGislEYKbjTr+xe5zdPsDrCxVAUJg6BrvwzINHbfXrqOW9Nf5YQBNooRz4IzQGzhwnBEePn6KKIywfuNaZs2KokAiEiJkVc32UQ8PHz+d6sY/DbPUl5395gRpAcCHGOychZX6Akxd52ubpT7Nuo+OmyV+LNlgaaHMy9+zzJsb9dpUEjLvl4Vpn4O3rbdLmOYKXBVcOlEjhDQA/JsA/haAv0xoEvOvAviN5C3/AMDfgCBqAt9iVMs2Plhr8NLkUq2MvWELlVIB9+/eQt4y8fkXmxOpAK2j7oTikt7ncq2KIAh5XxZTkph6s9aon6h6dAdD2LDw7MV+xtvsLCUsO2dBS6w4ojhGGIaIIhmESIiThvx8zkQYRRg6IwRhCEPXEMcxwpCGphNZBgjtSXM9H4qiwNA12PkcRq5HSZokwTJ0hGHEJzTpdfI4QZQlCZqiYDRy8eTZzswm/U63j2Ihx8uwACW5Wzt7Z35AzypXWqaOQt7iHnDj5bP1MZVvlvo0jQz6YYjNzW3cvFZPcjvpvQ+jiCc6pK090liqlXlJGMje24v0Z4neLgGBN4NLJ2oAfhvAfwWAzZ5XAXTiOGZmQzsArk3bUEDg2wBGekyDRgf5Qch7sgDaA8Ue0gC4D9dCpUgnFpMH+jhZsnMW9+iiU4QyFFnGUbcPx3UzTebbLw7w+RebGdUj7S22XKuiP3DOVS5bqS/ANDQQiUCTZMRAQpx8RPFxabHbG2Cv2UKr08XK4gJKxTw63T6WaxVUy8XEciLkvmuKLEPXVUpCUuXZUjFPhx58H0Zi38GUxFAiOOzQuKp0DuY40Xny1ddwXRruzoYGdvZenhjBdRLGhzQ2bq/x4HPLNPD46bOJezcNs9SncTK4Yis4bHfx6MkWVleWKDE0dIRRhJxpcGuQzecvMuee7pNjSN/bi/Rnid4uAYE3AxLH8envelMHJ+TXAfxaHMf/OSHkzwL4KwD+YwB/GMfx+8l7rgP4/TiOvztl+98C8FsAUK0ufO93/u7liG6mLsNxw9Pf+A7iXb82iiJzHzFJkqAqMiRJQhTHGDkOVE3nXlR+GEKV5cx7AcAPQm7HMBy5fAqS7VtRFMjSscuq61NFSibHr4VxzMtglqFn9p8+xnDkQpYk7iuXhuv5E+at6TWoigwiJeXMRFkDIZCSdXh+wJvg08ePAciyREuRccT7xkbOEIZhQkp+BwCEpi4hjmIEYQBCJD5BCtBsz6PegF+j9DrVhOj5fsB/r+sqVEWGH4RwUzYciiLz/Y7v6yQoioy8ZWauLbu+/aEzce/Gkb6/JyH970pRZBi6RsvfY/8/7w6GcF2fn48kS/wzlsb4vT3v+V9029eBd/3/OSdBXJuT8U1fn//oP/h3P4vj+OPT3nfZitoDAD8khPwaAAO0R+23AZQIIUqiqjUATP2aG8fx7wL4XQBYbtyI/9Xz6SHFbxrfvVHBZR37quNdvzZrjTqq9aWMm7uh6wBiPPzsJ1DzVTBK1G91YJeoGlGy88dZiolzvev52P3ZV9jaafL937uzjlq+xC0f9pqH6I8c/Onv3plYyx//yy/w+RebuHdnHbdWG5n9H7yiBre7z1+gOxji/t1GZlvT1LH94gC7r7I9W+z8AFpus5Mpyt5giBjA+0nQOYtx8oMQr1pHcEbuxDWhpbsQqqIiiiL88R/9IZZX11Et28hZBkauz4kes83odPsoFQtwRiN8sbk9VRG7d2cd1TGVZ7dFsyd3m5ON4uPvd1x3Ipt0VqP5WqOO9dtr/NoytDo97Pyrn03eu/Hy8ubOxPqnYfzf1Vqjju/ffm9iAnTrJ4+wtXP8Pu77NoYvk+GDtwHv+v9zToK4Nifjql6fSyVqcRz/VQB/FQCYohbH8X9ICPlfAPx50MnPvwDg/7i0RQoIXADdwTATTwUAI9eFP6Y0jDegu0lzf84yoSgyVyZaR91MduO0/qh7d9ZPXNPnX2yiP3TwS79wl66xf9xDlLa9YGtZqpWBmJbIapXSzJ6mtO3Ew8dPUbLzWK5VuLErgIzSxDzF7LyFgTOCpqpYrJagqgpV9XQVIDS/c7lWwWG7i+5giOXE4JcpQGwAYN4pxo0P1rC6sjS1R2v8/aw8XCnaPGEAmPTb29lvolGvIZ8zQchYhhTo/Rzv1broZGF623n9zUR5UkDg24fLVtRm4b8G8CNCyN8E8BDAf3/J6xEQOBeYQ34azD7D9X3sJAoWe1CmPaoYmWMkbeCMYOr6RK/YePP7zn4TG8O1DDkcDEfH7vgAdcwnNCSdGb4+erI1YcHQqNcyjefA/D1Nds7CV9t7GfIAALqm8v0xexAiEVRLRTpYkNh0SISgWMjj672XOOx0aVN+EtKuqWoyUGBNtRNhJMYu5DKvm6aOnGnAdX2+hvT5pHvH2HvZmkEoyfP8AO1Oj79v4/YaPtq4zUmoqii03y4MeeB6qzN9QOG8k4WmqeN+Y43/nJ4AZckUswiYsJ4QEPh24coQtTiO/xmAf5b891cAfvEy1yMg8Lrw8PHTCaUDoL1S6VIYkH2INlsdrF5bmtjuNLuDdJM5mx5Ne4Ex1WhcgUkTObYfO2dNDSJPr2HWg5+pOSy6iaHVyfqa7TUP8eGtmygX81ASskMAgBAosgRdVfHoZ1vY2aflSsd1cXvtOhYXygAATVXRHzhcFUuXFNNZnwANVwcmg9LZ+aQVKDtvwdA1BGGEQt5ERSnA0DXIsoyynaemvDFQtHNQZBkjl1o9+kGAdrcPxDTpodsfwtT1jGfeLMxDoKplO9NnxlS/vZctHlE1S2FkENYTAgLfHlwZoiYg8LbisN3F9ouDCdUpmtFozR6ijFCdJ3/08y82ObFh72dWHWnVyHHcxIxWRaNem3h4z2u5MO3BP0ttm5Y5unF7LVMyjOIYiGP0Bg42t3f5IER3MMRG0UbJzvMp0MVqCR9t3J4ISgcwkfVJ2NDFWHWSrYOteeODNRQLeZjJJKWuqRgMHWiqClWVoakKFEWBn0ynjic8aKoC16XlTrtAlT/T1E/0ZZvXEuUk1W9azuu7rJ69y+cu8PZAEDUBgW8A01Sn796onLjNRfuJGHm6d2d9wpuNId3Qf/u966hVShk15qJrmKW2jdtZxHEM3w/A/pcUxzHimBryVks2qqVjLzQ7b3GSxlDImWjUa5zQMSUNMSVhjCiPRh4GygjLtQovQY+fz85+E6srS7Q86oxQyFuUsCWkLXQjStRkCYCMkeuDS1npNeVNXLcXM6kPjuPik08/m3jvWSxRuoMhVor0ejCFEEASn6VnSPfrjHT6tuFdPneBtwuCqAkIXABn+cZ+nnLTWfqJZsX6pD29FFnGQtnGk2c7qBRtTtJURUHZzqNsUxVpe/eAP9TmWcP6jRUsVUs4OOxMTF6edN737qzjow9voVouQlFkRFEEPwgxcj34QTCh3JmmPkHSgOPM0u5giKWFMhYXyhmC5LrUFJcNPDBCs7WzN7FeVu51Ri463T7KxQKWFytwXI8Lca4i46g3QLc3nJhgHTgjNA87eP9mI7NWTVVQLhWmkq+z+Kodtrvwl3IwcTx0MhiOYOctvobVa0uZfFOGi0Y6fVvwJuKsBAQuC4KoCQicE9/UN/Z5CN6stTTqNeQsg8cLAVRtOux08fzFAW/kL9t5vq2uqVhdoZYbrFSXLseOpx388AffnzCO/b1PfnzqeVXLNlZXlmCaOqIoRBzLfIjAdT2EYTRR9nUcF6/iLkrFQoaIHXX7vPSZNsdlqFVKfBgBOJ5QjaaE0o+Tw/ZRj1qMBAG/Tke9Ae97Y7FQ6dgpO2fhZqOe2Y/nB4ijeCr5Oqurv+O42Hz8FHbOQqvTRaVoY3mRKrQDZwTHcbFcq2Z6Gxm+rZFOZ8HbFmcl8G5DEDUBgXPgsr+xj/d4zVoLQA1IJ0qFeQv9oUNloeTLAAAgAElEQVR9yFIkDaBlxEqpAF1TuR3Hzn4T9+/e4r1eACWDkiThzvs3qIlvYjq7fuMa1m+snOryb+csLC9WUEgeqn4QQFVVADGcpDF/aaHMPd4YfvzTR3A9D+/fvAaAoNnq4MlXX+Ow3cVao45en1qiMOIYBAFAstOmDNOI0LRy76MnWzOvQbqcm8beyxZXMYMwpPFYU2w6Zh3ztBIzI89bO/u4d2edlrZTxMz1fHrO5+hx/LZDxFkJvE0QRE1A4By4yDd2RrIU5WQH7FnlxnH1zDR1uh4CXopja9nZb054tnl+gG5/SC06ABCJQFFoz9XI9bmDPyurbXywhttr11EuUkLHers2bq+haOd5jFMYRfCTzNG1xvKpRE2SJSjK8f+C1CTdIAxCmIZOA9iT3Mq051mjXuNh7IosIZ8yee0OhvR80iQN9Lq0jrLTpicRobQ9CXCsLH7y6WdzlaIP211s7x5kypEDZ4TtFwenHvM8ze/TQuCdkXumc36bIPziBN4mCKImIHAOnPcbe5pkOZ2DmZYNs0qZ0wxZlxerUBUFURTBqwZ4+aqNg1dt/rB//PQZ7t15n5OXo14fdt7ipq9504ChqRh5HgxdhSzLeHnYhuO4fKpQVQJ+zJxpoFwqJAQkBiGE/wnDCFEUwXHdU0lHlKxF11R+3DiO4QchgiCATAi6/SG2dw/Q7Q34tf3+9zaQMw0EAVWpVFXB6soSN53VFAWyLMM0dHg+vR6s5+4sROg766u0fJhksbJ7MG+vIZu8HSd7J+G8thnzTti+S0TlXT53gbcLgqgJCJwD5/nGPm+5lPVupacW2fvGrRmqJRu6qiKKadnR0DUsLpQza2Hh5KxnydA1lO089fcydKiqgv7QQbvbh6YqKBby6PYoKWJeYkPHzZRPmSUEa+KXJAKAQFMVNA+pe386qmha/x5z0+/2adqAXchBVRT0h8dkV1fVDMFZa9T5pGO6rMgmHWuVEiWp/SG/fn/0Lx9zdS9NhE56iD/4eAMf3rrJfx4MR3ybeRVTtt+zEIRZAyHzkI15JmzfNbzL5y7w9kAQNQGBcyL9YJRkCVEYnfggn7dcev/uLbx/81qmWf7lYZsrM6wUmCY3nueDyJQwaaqCWrXE1bpq2cbu/ivsN1tYayzzdSzXKhmyE0fxsTGspmKhUkTJzkOWJVimzt8H0DIeIQZURcFRbwDL0CBLMnpDBz9//gKmrvPJStfzJ4YT2HVjjvp7TZqvlz4Gff0QwLEHXHcwhOv7meEIAHBGXuaa8ulOU8dStYROt58hPvfv3pooqaZjpJZr1cz+cpZBLT9OKW1fZMBk2rbAZFzVrP0J9UhA4O2EIGoCAqfgpAfgYbvLlRyGWQ/Tecql1bKNcqkwYeuwvFiF5wcYuV6SdUlgFywosgxCAFVVOMkJwwjFQg4fbdzG7feuQ1MUeowYsAsWur0hnwQ1dBUAoeXKkYdOt4+DZhs5y0AhZyIMI6iqAjufQ7c/QPuoz7M179+9hdvvNRCGIXqDEUaui71mC/3BEGvXV3hvVi7phWPDCZapY5hqcJckgsNWh1toMILnuB6GsYTvf7SRSVhodbrAjWt8e88P4Pk++kNnak4nYuC+aXLis3ptieeFskD68Rgp1p8HHCt3dt46sbR9kQGTaduuXlsCYkyN70pvZ+csrNQXJnrRhGeYgMDbAUHUBAROwGkKyVkezvOUS+2chTiK4fkBDF2FRCQA1Pw1baFhFyyoioz+0IGha9BUhbruhzFGrgdd07BQLiKKI/h+CM8P0B86IKAh7KzpP4piAPR4qkL7ulpH3URJO54WVVUFqqLgydbX/PypGkadxYIwpOXBGMjnLBTtPIIggKIofB9EIjBNHfVaBXsvW9R/LBV/5IxcOK6LzST/dLWiY2PjTiaz1M5bePRkCz9//gJ2niqD3f4QjkOtNtj1Zb11g+GIE53VlSU6/ZkyiWVKmTNyMzFSjkMzRRerx35s2oz0hvS9m/X6aURt2rZsneOTqvS9Hv9smoaO5cVjA19AeIYJCLxNEERN4ErgKpZt5iFhZ304p8ulJT3E55s7md+z0h4FJUFEkkBIxAO+ASAMQ+iqiqEzxNBxUSxQ9/z+wIHr+SgWcpBlGZFPHfM1VYGZ5FbqqorewIFpGlBkCXvNFiV3qsob91cWFzKqXhRFkGUJ/aHDr42p6zjq9Xm/2mJi+ur5ASxTRxiqCMOQW3doqoI4outhIefp+CNn5MLUdf4ZWF9azpA0gBKrfM6cyA9l125rZx/Vso0P1hoTapSuJTmffjbnkx17PEbKNHQUC/lEMXTw9e7LEwnQRSwhpr3H9f1pgQfoDoYoVXRUk88mO6+caWSsQ4RnmIDA2wFB1AQuHVc16mUeEnaehzNrcGYRUuMklZX2oihCBCD0osTKQuaTm64XQJb9xFLDw1GPljaHIxeKLEMiBGEYIo4jKLLMhw2CIOAEIAgCHPVGaHd6AKiJKjONjWOqsqXJWm/gcINYdm1YsLudt2AXcjB0DYoiQ5YkAODeagBQLOTgqLSXjHl8MaRD0k8jGP2Bg/7AmalMHra7+Bl2cN80M9u5ng8QcLWMkUTX8yeUTfb5G/cmO2l9F7GEmLbt9osDAJM9aoftLtYWlrLnlUBXj33ThGeYgMDbAUHUBC4Vl20cexLmIWEX9WuaRlJ391/h58UXmanPtUYdhZzFG+17gyH2Xh7C8wLEcQzX87FDgDjpQwMIcqYOmZMmGb4W4svNbW4ge5LH1l7zEIsLJTBJp9Pt4+vdJj939rdp6NBVlVpiSMy7LExKtxoQU7IWRvR1VZHR7vap0pXkMaXLk+l9M5KXVhIHzmhiIGFW7yAvgyY9b3vNQ07wGMF0HDeTbZrGNG+y9Pqm4SKWELO2nfZamCLAzsjFYDhCzjK4Wig8wwQE3h4IoiZwqbjKUS/zkrDzPpwVReblK4ZapYT+0OFTiwC14Ri5HkauD0NXucv9s519fLm5nTkuW8ettQY+vL0GLY4RJqVH3w+gaxo/n2arw7cfn1rtDxw4Iy8ZUIjgeQE/d3aMcqmAWqUIRZahqSokQo4J1dCBZWjQVBX9oYMgDBDHQKfXx4u9lzg47CAKI7Q608nivTvr0CVKQIpJb95es5UxjJ1mvZC+D59/sYkHH2+gZOfh+j5MnZaGHybRS6fdq/OS8ItYQkzbdtprQRBm1nbwqg3HdbG7/+pKtQ8ICAhcHIKoCVwqJkK3E/VDkqUz7edN9bjNS8LO83Bm5UEGdu55y8w8hHVV5dOJacuL3f1XE8dN/6zrGm+493yaU5mOUWKkcK2xnOltclzaK/b17kuYJlXMXN/Hzn4z08DeqNcgyxI8z6fDCKrM1S876ZHzgwCmocHzJegaoKoyRiMPVjKF+elPHk1cX6ayOp0D7ommayoeP312YtoBX1uy5m5/gCiK0en2+XtqlRJ29pvY2tmf6x5dZdPUq7w2AQGB1wdB1AQuFWnVYilpRh84I6w1lpG3zLl61d50j9ubMs1Ml6/YuQPUlmH7xQEePn6KRr0Gx3VRKVJLhrTSNk5y0w9tNrnIyBfL80z3My0tlDPHHTgjdPtDXF+uoT8coX3U4/swDT3jPWbnLd6/xqKaZFmCM3LhJT5nvQEdPNBUhcdMUaXumCgyBW988jWNkwLU0+deq5SOLTkArCxV+RBAGmdVa8fXd5XIkTB0FRB4+yGImsCl4/MvNrF+YwUlO88JBjBfr9pV7nE7Dax8tbqylCFLjuOiVikhnzN5WdAuWLDzFu8vGy/BTSOraVXO9f1ML5hp6JwUA7QPbHVlEVEUI4wilIrUy+3gVTtDoJnlRRqKLCEIaLnzydbXiCNaKmXZoK6iwDJ0hFGE/cTYlmEaaTrPgIads7glB7++YYhCzsyohen9nIdwnfVLwVUidQICAt9OCKImcCUQhVGmRMVwmvpxlXvc5sGs6cJysYDrVg2vOl04jsub35utzkRm5Cyy+vDxU+zsNzlRSBvz2nkLMQDPC7BYNVHImdA1FTFoE7/nB2gs10AIgWXqXG3LmQZyloH2UZ9PhbIYqYEzwpeb2wAAy6TJATnLQBAEGI6yaiDDNPLFVNZ8qjJ8Wm9YdzDM+KMBlAg7Iy8zCZnugTurCnvWLwVXdZpZQEDg2wVB1ASuBE5TUWYpExfxrjppv6f97nVifLpwaaGMatlGEEZYVhVuZOo4Lrq9wcRaTiKrWzv7vO+r2xvwnjQvCJADsLxURT5nQlFkgBAgiiERAiUJSC8XC+gPHW6kylS1OI7x8lUbmqai16feb+lGf5YCMG3ikmF8OCF9nT//YhP312vYTcxvT7s3h+0u9pqHqJQK/D2sr29rZw9RGE30wKUxjwp7li8F32alV0BA4GpBEDWBK4GTJuxOUiYuYo9x0n6/STVk3EoiZxnoDYZQFfrPM21kOo2AnkZW0+diGjrsgoWDZhuLlRIKlglFlgEQxHGMMKIGtYQQIAb6gyFUVeHHZ8re9osD7rk2jcyycvZ71+toHXXx5eb2VFJ20nUOghBbO82J85q1TSZ83vPhjFw0W53MAAIzw03nfDKcpsKe5UtBo17j06bzeLCdF6K0KiDw9kMQNYErg2lTbPMoE+eZfjtpv+y/TzrmrH2e96HJiM2d9VW0u320O71Mo7+dtyac+BlOIqvj56lrKnKmgXKpAD8I0Bs6sCUCCQSKKoMk5mZxHMP1fbxqd2HnrUz5cPvFQYa0zir7bdxe4+u/2ajj0c+28PkXmxl/sLNe52rZxuq1JT6Jyvr52DbTpkjTa2JTocu1ClfcGE5TYef9UnDvzjpWV5a4upeOdnqdJrSitCog8G5AEDWBK4XTJgDTr8+ypZgHJ+33pG1mHWPWQ3Ne8sa2J0RC2c7TRv4mteOoL1bgedSf7P7dW1MfyLOONX4+bOoznzTdj0YuZEmCLEkwoEECAEnCcDjC3stDvs3m9i46Rz1ONNYa9ZnnVC3bmQEJRVFQLdm4/d71TH/defoL79+9xQPVgWMSlN5mlr8auz88mSCV8zmvCnvaPeXWIikTWqaIpkvDF8UsDz5RWhUQePsgiJrAlcZFe9Be535n/W6WMvTg440JM9dpikeGRKQe8KZJtx0mVhnpfc8KfT9tgpLt3wsClFU6lfnyVRvdwRB23kLzsAM9SRSw8xYP+66WbERRBLuQO1XFsXPWcf6kRYcKJIlgrbGMf/sHD/DZoyfY2W+e+R5UyzZMQ8+8xkjQaZ+HcVLISriH7Q5+trVzIbuOWcdJ+96Nq5AXxbgHX/r4gqgJCLxdEERN4ErjIj1o590vK3+mbR1OOuY0Zcg0dZTs/ITZ6jSCNUEikgf8YbuDQVLam3bMecuw4+f56MkWdvabGV80IFvSXL+xgvt3b2XsUlavLU0EnU87p+5gCNfzoSgKNFWBqirQFAWEEOQsHUu1CvabLfz00ZMz3Vs7Z3GiWbTzPPfUcdxTPw/TiJzjuJyksevFEhpOU0DnHW5hk66sn+91Ie3Bl4bI9xQQePsgiJrAlcebcmBPPzxZSS5TwqQxlzOzIBmmPRx1Vc2YyzLM6xvmjCiJACb75WZtwzBehnVcl09hpkuPn3z62czrOs0uhdlfnNaEf9juYnv3AMuLFUgSnSAlhIAQAolIMHQN9VoFH23cwu998uOMhchJ11mSJZTsPDRNBb85iOG403v30phFzAHg3/rB92HnLGiaClWReTl1lgL6poZbzoLxCKk3dRwBAYHLhyBqAt8KvG4H9vGHLUOG4IxOJwBsbeMPzb3mYabsyTArTYDFNjEwEjHrdyc122esPhKn/r2XLX4+8/T2dQfDTHyU47g08DueeOtU0vj5F5voDx386vc/QtkuwNBVqEmSQRxTC5BCzkKjXssMGMwCu1+FvIXFagmeH2AwdDAYjmDq+qkDCHbOws5+c8JX7oc/eIDFagmSRCDLMjfzNU19qlr4poZbzgMRISUg8G5AEDWBdw6zHrazME/fz7SH5jTlJb0f09Rxv7HGf06HajfqNdy/e2vq7+b1+ko79bOMz1nkY/xh36jXYOesTGLCo59tTVwrx3X5McfXtfl8F/VaBffurEPTaDk5jmPEcYwojhGE4YnXlGH9xgpu3WzA9Xz0+kOYhgZFltE+6vPevVn36KQhj9VrSyjkTACARJKBCp0qoWzKdXy/b2q45bz4po4jICBweRBETeCdw0mTndMwb9/P+EPzJMWjWrahynJme1M/boofJ47sd7OmLNMZnwxpp/50GTZNKqYRGWbAOx4C3x86iMKI/71SX4Cp61i/cY1vO14qZN5m976zjoVKEYQQhFGEkevhqDs4tXfr3p113LrZ4FYXfhAiSP7E8bG8N+0enaR+2TlqOcJSFaI4AiBDIhIUWaLq4ZT9vqnhFgEBAYFZEERN4J3DrIcqIw2n9f2cpdyUJm/p7V6XPchJGZ+MbKQzPoFs2sNpyiJrhl9aKOP+3Vu8b228HMu2nVaC/PQnj/Dl5ja+/9EGFipFeJ6Pbn+I7d2T7SqYBQU7DwBQFRl+EEBVFE4+Z5WCT7rG3QFNUwiCgEdhhVGEKI7QGzhwnOmWHd9UD5qAgIAAgyBqAu8cTnrYTnPPT+PenXVuuEokgnanh4ePnwKY7tCf3m68ZAinM/G+cRKZVrTSv6uWbTTqNayuLE1MYaYzPlud7sz+Nu6en7j4M+RzZuZ1lpaQPv5yrTrhus+uwbTzP2x38Q//8Y/PRHKZBQX3PUvKuL2+g73m4aml4JPUr8N2F9svDmDnKZlzFQVBEODZzj6ebu2cuF/RGyYgIPBNQhA1gXcSJz1sxw1Z04rYxgdrSTA59Qfz6jVcX67BCwLuPj9eApymXJm6jsEw25nP+r2YpUba2X/gjNCo1zK9byU7j0qpMOGwn8743NrZn3qejHBy9/xkH0sLZRpwrqt8367nY+CMMqTM9Xza9+acHrKexll6qtIWFMz3TFdVPHz8NBMLddKxTlK/Pv9iEzv7TTTqNQCYCLt/XechICAgcBFcKlEjhBgA/gCAnqzlf43j+K8TQtYA/AhABcBPAfxmHMfe5a1U4G3E+MOWERrWe8XAiFejXkPONLg/GAAYuopSsYDB0OG+a+MlwFklON8P8PDx08wxWb+X47rcjywdlbR+Y4UTD1YSTDvsA5Nkadp51iqljFKVswyUiwWAUAXLcVxOjDa3d1Et2Zl9OiMXraPZat3rwLgFheO42H5xMBdJY5hmwZLG20S4hMonIPB24rIVNRfAr8Zx3CeEqAD+P0LI/wXgLwP4O3Ec/4gQ8vcB/EUAf+8yFyrwdoPnQBo6d+NnClk6AxQAFPnYFV4iEphnRToP085ZKNl5LFVLcNxJPzWAKkbsgbqu6xk7DBboPe5ltlRNlU9TRItNdc5DljLu+SmlavxYjLB1jnqIouhCEVnnxUWOMc2C5aoTmNd1riL3U0Dg7cGlErWYjm2xp4Oa/IkB/CqA30he/wcA/gYEURO4IE6awGQPOR59lEQTpYnXzn4TG8M1KMrxPxvX9+EmOZzppveP730HZTvPfw6CENu7L/nPzVYHURDyfTO/MwDJ/mMc9QYTpcWDww7WGubxzwnR2n5xMHfpbsI9PyFkWzt7WGssT33/rBJquq/vpPzPi+A8qtd5At8vG+clW9/GcxUQEJgfl62ogRAiA/gMwPsA/jsAmwA6cRwHyVt2AFy7pOUJvCU46SGYVpjSNhZphYwRkEdPtrC6soT6YgWqIuOoO6BvTkqGACBJJEPSADrBeNjp8mDzw3YX371Bw8UlWeIkjfW+AUAQRliqIdP7tvl8F3nLzJzLeXMkxyOypu07rdDNIkwPPt6gwwXJ8MFF1Jw0GbwIzhP4fpm4CNn6tp2rgIDA2UDSXkSXCUJICcD/BuCvAfgf4jh+P3n9OoDfj+P4u1O2+S0AvwUA1erC937n716O6GbqMhx3PvPOdw3nvTaKIkOWJIRRhCC42LVVFBmWMZkSMBy5CIJw4veKokCWCPwgRBRF8MMwo2yxtYEAiI+b3tl6DV2dmkrguC76gxH/mV0bXVORs0zIssQnHeM4hucHiOMYru8jiiJ+LLbm81wf09S5f5skSYiiiF+H8fObZ9/5nAlT1/jPYRQjCIKJfZ51bQAQhj4GzvSy8WmYds8lifqj+X5w4c/U64auqVzNTeP/b+/uY+u66zuOv79+yPW1E8+O49pJTdM067pm7dJAhzqYEFCKYKso02CjgqlDTIWNaTCBtm6TNsFAAmliwNiQIsroH6w8lEJR/0DrujLYUyfakLU0hChNU5zEjhvbOLGvb/zw2x/nnJtzj++jfe855977eUmR7evre3/354fzyff3lL+8UvIosvDvVbWf706jv8flqW8qi7t/3nX3259yzt1a7X6JV9QCzrl5M/sucBswZGY9flVtAig5e9g5dxg4DLB7Yq975vRsXM0tcvPenST13HHazPyZzfTNwRv3M9LA+Tb7JsYZGR/bcPvZ02c4NTlTeM7o9hlnZ6qfBFDKoV+6nl85eDOra+usrq4Wbn/8v57mZKgvgr4ZGR7k0IEJxnYNMzI8yOqat6HruZlZcrk80UvwzOw8RzbRHyPDg0UnIQR+XOUs00qP97oDP19YORo4d36Ws8efL/TtZtuWm5/m7EJu01Wh8Pd0bNcwGGVX5iYt+BmIKve9if5elawYn5xsTmNTrlP+Hm+G+qaytPZP0qs+R4EVP6RlgTcAnwSeAN6Gt/LzHuCR5FopEN9k5WbMt6llN/lGTYw/eON+Roa8sLVjoL9wJuXUzGzZ1YrBNhLBfmVAYTuMbF+maFgVNt8f9Q6RVeuPwYH+onl5gcy23rqHLpsxfBd8TyfGR4uGeSF9c7i2upGu9nYTaV9JV9R2Aw/489S6gK855x41s+eAr5jZx4AjwP1JNrLTxTlZuRkX7FovglvdqiHcTz95fpLhoR0MZPs4euwkR350ouLXBnt6vfoVN7Fjez8Ll7ygk1v2tskIVoGGFzfU29Z6jj+qFMyDQNDV3bVhM1rwDqRvZtsqiYaVC3ML3sH2kUUZkL45XFsNW+201YiIXJH0qs//Aw6VuP154JXxt0hKiXOycqULdvQiVs9FrdRFcCsXxVJfG+2nufmLzM1fZN4/OLyaifFRlnJ5nPOqUrPz3uNed82VlZjBtiG1BphoO2sJrJWC+cT4aNHn+rOZoi0+zs1cKJzvWY9SbVtZW2vIFhVJnc+5mZ8vhS0RiUq6oiYtIM4LXbkwUSogLIWqJLUMxYYvglsZym1GIAiHo9xyHgyuvXqcy6urLC4tF4ZEB7J95PL5mi7m5dpZy5BmKdHvAcCSv63H+tr6lofcom3bM1j7n6dqVd+4z+fUvmYi0igKalJV3Be66AUb4NCB6wufz2YzjI/u5Nz52cJu/PUMxW5lKLdZgSAcjoI91fr81ZQX5hc4d36WwR394ODSYm7Lr7FSm+oJ4NlshrGRIY6fmmzIz0O4bXsGd9b8ddWqvnHO4dK+ZiLSSApqUpNGX+iqPVb4gr1vYrzoc5lebxuDYDf+QK1DsYMD/UWnANQz72szgaCWfgvCUTabKcz3Wl1bA4yBbB/benvp7fG2rrhmj7eCtVKFplJVrFpbygXOyamZotsKm/Q6OJTNJlo1qqWaGdewovY1E5FGUlCTmjXqQlfvsFD0IhysNIzuL1VrJWjP+C52j16p1gTzvrq6u6rurl9vIKj1tQbh6Pprr2zREGym+3OD2+nLbGM5f5nFpWVyy1fOEwWKKo/B+6XaOTY6XHQmaKV+LxfMgwAXBMqgPZBs1SiJ4c1ykpoTJyLtSUFNYlVuWGj/3j1l5zlFL8K5XJ6pmdmialqtF+WR4UGymcyGeV/Dkb3AqgWqWgJBvUNgR4+d5NJSjkMHri/s8h+2cGmp6LbwcHCpfcJmZue55uoxMr29WJeBo+jrqwWrUsE8CHA37JvY8HiQbNUoLVtUpCk0ikjrU1CTWJUaFhrbNczQ4PbCoeClQlKtQ4q1TpSffmmObF+GzDYvxLj14hM6qgWqWgLBZobASh3j9MKZqQ0nHWSzmUJQCu+/FuwXNrpziFw+H5wXz/ZsH729PRv2E9tMsLowt8BxJjmUzW74XLmqUVwBKi2rJtMSGkWk9SmoSayiF/IgZIRvLxeSql2EaxlmDD9PbjlPbjnv7VFW4pieSiEmaEulw8g3OwRW6iK/4eSEUNgKHz0UnE8a7L02v3CJwe3enLwdA/309PTws4uXCpW3zQ7H1VM16tQVkGkJjSLS2hTUJFbRC3xmW29hF/6wapWeUkc+RatOpQJfqYBxbuZCybM5q4WYcBuCStWR0JE/WxkCi17kK62EDYfMYP5epreX/OWVQhBeXV3j8soqPf4B8NlshhfPTG8pSExOzRS934jhXxERKaagJrELhw5vAv/uDfepFJJKXfx3j46UnNdVKvDVUrGqFqjCbSisfsSrEL54drpQMWrkEFg0vAUhMLecZ3FpueioqSB8Dg1uL9x/cSnH3MIl3LrjxTPTW6pqRfsraF9Us1ZAalhRRDqFglqHScsFLhw6onOyqoWkUhf//MrKhu06oHzgq1axqnWbjvB2GuBVCKMVo2YNgYXbfOS5E4V2hcNntu9KpXAxt8zcvHdKQrgaVq96qmTNWAHZqUOpItKZFNQ6SFovcPWGpFIX+Vwuz+z8QtEQZr0r7eoJVEEbgj3dAsEwZFyrH6NtjobPyakZDh24vmgRwVZXINZTJWv0Csgkh1LT8p8cEeksCmodIu1zheoJSeUu/nGutAvakM2GKlahPcXSsmfWhbkF/vU/n2pov9RbJWvk9yWpzWTT+p8cEWl/Cmodot12Sy938d/sMONmgkRRxSqykWz4McptK9LTs1Z3OzerEcOv4ddRb5WsUcO/SWwmm/b/5IhIe1NQ6xDtuMLg+GwAABKISURBVFt6UiclRNtQqWIVfezwYfK5+WkO3ri/JSozpfroyHMnYh8KTGIz2Xb7T46ItBYFtQ7RSrulN3P4slR1q1K1pNa2lAqN0cfO9vmHyc/MFuaLlToKKm3fk3J9NDk1w6nJqdjbE/dmsu34nxwRaR0Kah2kFXZLb+ZcoFKPvXBxseR9Bwf6mRgf3VJbopWYYGPaYFPaQPgoqM08T7OlsaIUx2ayWxnqFRFpFAW1DpPm3dKbOReo3GNfWsqVvH9Xd9eW27LhMHl/RWiwKS0UHwUVfR5IR5WtEytKaRnqFRFRUJPU2GrlplK1sNxjr6+tl6yWrK+tA16QyvT2kl9ZIZfL11VFig4355b9w+T9alpXVxd923pYzq9u+Npaq2xxVEhbadi8EdI21CsinU1BrcnSPtSYJlup3FQbMg0/Rjh8LSwucWpyquTctfCJA+BtGBtsLFurcofJB0Fs+fIqu6/ayeLSMtMveedvZvsyRacMQOlqXpxbRrTCsHnUZtubxqFeEelcCmoNFr44bHWOU1o164K92cpNLUOmwWPfdMO+QvhaXFpmYny0MBy84XkclT+u43WVeg3r6+vkcnkWc8sM9PcVtviInq4QCAeFOLaMiH6fGzVsHkfg20qI7cShXhFJLwW1Bio6pLsvw+COfqZn5gqfb4e9l5pdxdlM5abWCsjk1AzX7Bkjn18pnAta7nsyONDP9EtzZPsyZLb1Fu5fT1Wl3OuItnd6Zo5sNsOFuXmOn5oENg59QnFQaHbVp1nf5ziqgFsNsZ021Csi6aag1iDRi0NmWy8D2b6io3ugtYdPGrWVRTX1Vm5qrYAMDvSXrFiV+p4EXxu9f61VlUqBpNwRWMdPTRbaUS0oNLPq06xqXVwbxzYixLbiUK+ItCcFtQaJXhyCFX7RrRhaefik0gUwyWHeWisg9YSbrVRVqgWS4LG3d135fPSxqwWFZlZ9mlWti2vuV6NCbJpXSItI51BQa5DoRSC3nGdxabloK4ZWHz4pd6GrtJVFo5ULL0ePnWT/3j2MjQwxfWGek6fPbvjaesPNZqsqtQSSo8dOcmj/KGdPnyn72NWCQrOqPs2q1sU190tDlyLSThTUGqTUxeHZn5xicmqmbYZPyl0Ag60sorzAcrlhz19pODH8uX0TWbb3Z0tW9OoNN5upqtQaSFZX1zg1OVPXY0c1o+rTrKATZ4DS0KWItAsFtQaqdFB4nJp5gSq33UQpC4tLbB9szI9YpeHE4P1Sn9tMpWqr2qGi06ygE2eA0tCliLQDBbUGS/riEMequuhrrBRM9gzubMhzVhpOrPQ1SX0v2qGi06yf5aR/R0REWomCWhuJa1VdKc0OJtWGE6MnCFT6mrg0I5C0evgTEZH6KKi1kaR3VG9mpaRS1e7gjfsZHOhnoN/fyDa3zLPHT7VdkInzJAIREUkHBbU20u47qpebHze6c2jD5rSTU1ubpJ825aql+/fuYX1tXRU2EZE2paDWRlp5EnutQ3rRql24ihjenDauKmJcQ5GlqqVjo8MMDW5nfuES0NwKW/A6u7q7FAxFRGKkoNZmWnESe6ueyxjnUGT09WSzGQayfSxcvHJ7s+YjBq9zbNcwA/19LOaWmZ6Z09CriEgMuqrfpXnM7GVm9oSZHTOzH5nZB/zbd5rZY2Z2wn87nGQ7W82FuQVOTU61REirtu1GNUEVMSyOKuJW212v6OvM9PayuLQMwNDgdrJ9GaDyKtjNCF5nti9TmAMYHI3WzNcrIiKepCtqq8CHnHNPm9kO4Ckzewz4PeBx59wnzOw+4D7gzxJspzRJq57LmMTCjfDr7Oru4rZbDrD7qivbnywuLXPkuRMNfc7gdWa29RbdHhyN1spn14qItIJEg5pz7hxwzn//opkdA64G7gJe69/tAeC7KKilTi3hqKenm30T42Xv06rnMiY15Bq8zpHhQbDIJ6MfN0DweoKzawPB0WjtslBFRCStkq6oFZjZtcAh4ElgzA9xOOfOmdlVCTZNSqhlftbBG/fT35VnZHys7H1adQFE0u0eHOhnemZuw/5xja5whV/n4tJyYY5aLpdvie+TiEirM+dc0m3AzLYD/w583Dn3sJnNO+eGQp+fc85tmKdmZvcC9wKMjOx6xWc+9/nY2hyWzXSTy68l8txJ6Onppt+fExW2tJxndXWt6D7ra6t0dfeUvE/0Mbu7ulhbXy/5+bTaSru38nNTy/egkYLXiQGOWL5PnfZ7VQ/1TXnqm/LUN5XF3T/vuvvtTznnbq12v8QrambWC3wD+LJz7mH/5mkz2+1X03YD50t9rXPuMHAYYPfEXvfM6dlY2hx1896dJPXcSdg3MV6okoWdPX2mcMh4cJ/c/DTZobGS9+kElYaHt/pzU7KqeXJy04+XNp32e1UP9U156pvy1DeVpbV/Eg1qZmbA/cAx59ynQp/6NnAP8An/7SMJNE/KqGV+VrtvvluLZm/f0YpbsYiISH0S3Z4DeDXwu8DrzeyH/r9fxwtod5jZCeAO/2NJiVq2xEhq24y0iGv7jlbaikVEROqX9KrP/6D8WrXb42yL1KeWas7RYyc5tH+Us6fPdFzFJ+lzV0VEpD0kPkdNWlctW2Ksrq511Jy0gIZ+RUSkEZIe+hRpS50+9CsiIo2hippIk2iyv4iIbJWCmkgTxX1igoiItBcFNdkUVYpERESaT0FN6tbs/cFERETEo8UEUpe49gcTERERBTWpU6X9wURERKSxFNSkLtofTEREJD4KalIX7Q8mIiISHy0mkLqlZX+wpNqQhtcuIiKdQUFNNiXp/cGSWnmqFa8iIhInDX1Ky0lq5alWvIqISNwU1NrYyPAg+ybG2y5IJLXyVCteRUQkbhr6bFOlhugmp2bqmluV1rlYSa081YpXERGJm4JaGyo1RHfTL+zjmqvHyOXyQPW5VWmeixWsPA23L5fPFypblULlVsJnqefVilcREWkmBbU2FB2Ky/ZlGOjvI395pRDUgrlVpUJGpblYaQkl4ZWne8Z3kc1k2L/3aqB8qGxE+EzLilcREekMmqPWhqJDcZltvQDkV1aKbq93zlXa5mJdmFtgYXGJbCZTdHupCf6NXAhwYW6BU5NTCmkiItJ0CmptKLopbf7yCou55UI1LVDvnKs0zsWqNVS2SvgUEREJ09Bnm4oO0U2Mj9Y8t6qV5mLVGipbKXyKiIgEFNTaWHhT2gtzC3XNrao2Fyst87RqDZWtFD5FREQCCmodpN7TBMrdP20rQmud4K+FACIi0moU1KQuaV0RWmsITfroKxERkXpoMYHURZPyRURE4qOgJnXRpHwREZH4KKhJXaJbf4Am5YuIiDSL5qhJ3TQpX0REJB4KarIpmpQvIiLSfBr6FBEREUkpBTURERGRlFJQExEREUkpzVGrkSbPi4iISNwSDWpm9kXgTuC8c+4m/7adwFeBa4EXgN92zs0l1UZI35FJIiIi0hmSHvr8EvCmyG33AY87564HHvc/TkylI5NEREREminRoOac+x4wG7n5LuAB//0HgLfG2qgIHZkkIiIiSUm6olbKmHPuHID/9qokG6Mjk0RERCQpLb2YwMzuBe4FGBnZxc17dzbleRYunKW3u7vw8craGnsGe9gz6D1fNtPdtOdudeqb8tQ3lal/ylPflKe+KU99U1la+yeNQW3azHY7586Z2W7gfLk7OucOA4cBdk/sdc+cjo6iNk6lVZ83791JM5+7laW5b5JeyZvmvkkD9U956pvy1DflqW8qS2v/pDGofRu4B/iE//aRZJvj0ZFJ7UUreUVEpBUkOkfNzB4E/hu4wcwmzew9eAHtDjM7AdzhfyzSMFrJKyIirSLRippz7u4yn7o91oZIR6m0kldVUxERSZM0rvoUaSqt5BURkVahoCYd58LcAjOz80W3zczOq5omIiKpk8bFBCJNd/TYycRXfYqIiFSjoCYdSyt5RUQk7TT0KSIiIpJSCmoiIiIiKaWgJiIiIpJSCmoiIiIiKaWgJiIiIpJSCmoiIiIiKaWgJiIiIpJSCmoiIiIiKaWgJiIiIpJSCmoiIiIiKWXOuaTb0BBmNgOcTujpdwEvJfTcaae+KU99U5n6pzz1TXnqm/LUN5XF3T97nXOj1e7UNkEtSWb2A+fcrUm3I43UN+WpbypT/5SnvilPfVOe+qaytPaPhj5FREREUkpBTURERCSlFNQa43DSDUgx9U156pvK1D/lqW/KU9+Up76pLJX9ozlqIiIiIimlipqIiIhISimo1cnMvmhm583s2dBtO83sMTM74b8dTrKNSTGzl5nZE2Z2zMx+ZGYf8G/v+P4xsz4z+18zO+r3zUf82/eZ2ZN+33zVzLYl3dakmFm3mR0xs0f9j9U3gJm9YGbPmNkPzewH/m0d/zsVMLMhM3vIzH7s/+35VfUPmNkN/s9M8G/BzD6ovvGY2Z/4f4ufNbMH/b/Rqfybo6BWvy8Bb4rcdh/wuHPueuBx/+NOtAp8yDl3I3Ab8H4zO4D6ByAPvN45dxC4BXiTmd0GfBL4O79v5oD3JNjGpH0AOBb6WH1zxeucc7eEtg7Q79QVnwG+45z7ReAg3s9Qx/ePc+64/zNzC/AKYAn4JuobzOxq4I+BW51zNwHdwDtI6d8cBbU6Oee+B8xGbr4LeMB//wHgrbE2KiWcc+ecc0/771/E+4N5NeofnOeS/2Gv/88Brwce8m/vyL4BMLMJ4DeAL/gfG+qbSjr+dwrAzAaB1wD3AzjnLjvn5lH/RN0OnHTOnUZ9E+gBsmbWA/QD50jp3xwFtcYYc86dAy+sAFcl3J7Emdm1wCHgSdQ/QGFo74fAeeAx4CQw75xb9e8yiRdsO9GngT8F1v2PR1DfBBzwL2b2lJnd69+m3ynPdcAM8E/+sPkXzGwA9U/UO4AH/fc7vm+cc2eAvwVexAtoPwOeIqV/cxTUpOHMbDvwDeCDzrmFpNuTFs65NX8YYgJ4JXBjqbvF26rkmdmdwHnn3FPhm0vcteP6xvdq59zLgTfjTSd4TdINSpEe4OXA551zh4BFOnAorxJ/ntVbgK8n3Za08Ofl3QXsA/YAA3i/X1Gp+JujoNYY02a2G8B/ez7h9iTGzHrxQtqXnXMP+zerf0L8oZnv4s3jG/JL7+AFuLNJtStBrwbeYmYvAF/BG374NOobAJxzZ/235/HmGL0S/U4FJoFJ59yT/scP4QU39c8Vbwaeds5N+x+rb+ANwCnn3IxzbgV4GHgVKf2bo6DWGN8G7vHfvwd4JMG2JMafV3Q/cMw596nQpzq+f8xs1MyG/PezeH8ojgFPAG/z79aRfeOc+3Pn3IRz7lq8IZp/c869E/UNZjZgZjuC94E3As+i3ykAnHNTwE/N7Ab/ptuB51D/hN3NlWFPUN+AN+R5m5n1+9et4OcmlX9ztOFtnczsQeC1wC5gGvhr4FvA14Br8H4A3u6ciy44aHtm9mvA94FnuDLX6C/w5ql1dP+Y2S/jTU7txvsP0teccx81s+vwqkg7gSPAu5xz+eRamiwzey3wYefcneob8Pvgm/6HPcA/O+c+bmYjdPjvVMDMbsFbhLINeB54N/7vGB3eP2bWD/wUuM459zP/Nv3sAP4WSb+Dt1vBEeD38eakpe5vjoKaiIiISEpp6FNEREQkpRTURERERFJKQU1EREQkpRTURERERFJKQU1EREQkpRTURERERFJKQU1EBDCzITObN7MLwSazkc93mdlDZubM7AtJtFFEOo+CmogIhaO9Pou32eUflbjLZ4HfAh4F3htj00Skg2nDWxERn39Y8wvACnCtc+6Sf/tfAh8D/ge43Tm3lFgjRaSjqKImIuJzzs0Bfw+MAO8HMLN344W048CdCmkiEidV1EREQsxsJ3AaWMYLa18GZoBXOedeSLBpItKBVFETEQnxD6j+HLAL+CqwBLxZIU1EkqCgJiKy0aOh99/pnDuaWEtEpKMpqImIhJjZHrzhzsCBpNoiIqKgJiLiM7Mh4DvAXuCvgEXgw2Y2kGjDRKRjKaiJiABm1gc8AtwMfNQ59zfA54FR4A+SbJuIdC6t+hSRjmdm3cDXgd8EDjvn3uvfPoq3r9olYJ+25hCRuKmiJiIC/4AX0r4F/GFwo3NuBvhH4Crgfck0TUQ6mSpqItLRzOwjePPRvg+80Tm3HPn8VcAp4CJeVS0XfytFpFOpoiYiHcvM3ocX0p4F3hINaQDOufN4c9XG0BmfIhIzVdREREREUkoVNREREZGUUlATERERSSkFNREREZGUUlATERERSSkFNREREZGUUlATERERSSkFNREREZGUUlATERERSSkFNREREZGUUlATERERSan/Bw5jlbDvOX69AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import utils\n",
    "\n",
    "# Set the default figure size\n",
    "plt.rcParams['figure.figsize'] = [10.0, 6.0]\n",
    "\n",
    "# Set data range\n",
    "data_min = 10\n",
    "data_max = 80\n",
    "\n",
    "# Set the amount of correlation. The correlation is anumber in the closed interval [0,1].\n",
    "corr = 0.8\n",
    "\n",
    "# Create correlated data\n",
    "X = utils.create_corr_data(corr, data_min, data_max)\n",
    "\n",
    "# Plot the correlated data\n",
    "utils.plot_data(X, corr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mean Normalization\n",
    "\n",
    "Before we can apply PCA to our data, it is important that we mean normalize the data. Mean normalization will evenly distribute our data in some small interval around zero. Consequently, the average of all the data points will be close to zero. The code below uses the `utils.mean_normalize_data()` function from the `utils` module to mean normalize the data we created above. We will again use the `utils.plot_data()` function from the `utils` module to plot our data. When we plot the mean normalized data, we will see that now the data is evenly distributed around the origin with coordinates`(0,0)`. This is expected because the average of all points should be zero. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import utils\n",
    "\n",
    "# Set the default figure size\n",
    "plt.rcParams['figure.figsize'] = [10.0, 6.0]\n",
    "\n",
    "# Mean normalize X\n",
    "X_norm = utils.mean_normalize_data(X)\n",
    "\n",
    "# Plot the mean normalized correlated data\n",
    "utils.plot_data(X_norm, corr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PCA In Brief\n",
    "\n",
    "Let's go back to the example we saw at the beginning. We had some 2D data that lies close to a straight line and we would like to reduce this data from 2D to 1D by projecting the data points onto a straight line. But how do we find the best straight line to project our data onto? In fact, how do we define the best straight line? We define the best line as the line such that the sum of the squares of the distances of the data points to their projected counterparts is minimized. It is important to note, that these projected distances are orthogonal to the straight line, not vertical as in linear regression. Also, we refer to the distances from the data points to their projected counterparts as *projection errors*. Now that we have defined what the best straight line should be, how do we find it? This is where PCA comes in. For this particular example, PCA will find a straight line on which to project the data such that the sum of squares of the projection errors is minimized. So we can use PCA to find the best straight line to project our data onto.\n",
    "\n",
    "In general, for $N$-Dimensional data, PCA will find the lower dimensional surface on which to project the data so as to minimize the projection error. The lower dimensional surface is going to be determined by a set of vectors $v^{(1)}, v^{(2)}, ...v^{(k)}$, where $k$ is the dimension of the lower dimensional surface, with $k<N$. So for our example above, where we were reducing 2D data to 1D data, so $k=1$, and hence the lower dimensional surface, a straight line in this case, will be determined by only one vector $v^{(1)}$. This makes sense because you only need one vector to describe a straight line. Similarly in the case of reducing 3D data to 2D data, $k=2$, and hence we will have two vectors to determine a plane (a 2D surface) on which to project our data.\n",
    "\n",
    "Therefore, what the PCA algorithm is really doing is finding the vectors that determine the lower dimensional surface that minimizes the projection error. As you learned previously, these vectors correspond to a subset of the eigenvectors of the data matrix $X$. We call this subset of eigenvectors the *Principal Components* of $X$. We also define the first principal component to be the eigenvector corresponding to the largest eigenvalue of $X$; the second principal component as the eigenvector corresponding to the second largest eigenvalue of $X$, and so on. If $v^{(1)}, v^{(2)}, ...v^{(N)}$ is the set of eigenvectors of $X$ then the principal components of $X$ will be determined by the subset $v^{(1)}, v^{(2)}, ...v^{(k)}$, for some chosen value of $k$, where $k<N$. Remember that $k$ determines the dimension of the lower dimensional surface were projecting our data to. \n",
    "\n",
    "You can program the PCA algorithm by hand, but luckily many packages, such as Scikit-Learn, already contain built-in functions that perfrom the PCA algorithm for you. In the next section we will take a look at how we can implement the PCA algorithm using Scikit-Learn. \n",
    "\n",
    "\n",
    "# PCA With Scikit-Learn\n",
    "\n",
    "We can perform principal component analysis on our data using Scikit-Learn's [`PCA()` class](http://scikit-learn.org/stable/modules/generated/sklearn.decomposition.PCA.html). Scikit-Learn's `PCA()` class uses a technique called **Singular Value Decomposition (SVD)** to compute the eigenvectors and eigenvalues of a given set of data. Given a matrix $X$ of shape $(M, N)$, the SVD algorithm consists of factorizing $X$ into 3 matrices $U, S$, and $V$ such that:\n",
    "\n",
    "\\begin{equation}\n",
    "X = U S V\n",
    "\\end{equation}\n",
    "\n",
    "The shape of the $U$ and $V$ matrices depends on the implementation of the SVD algorithm. When using Scikit-Learn's `PCA()` class, the $U$ and $V$ matrices have dimensions $(M, P)$ and $(P,N)$, respectevely, where $P = \\min(M, N)$. The $V$ matrix contains the eigenvectors of $X$ as rows and the $S$ matrix is a diagonal $(P,P)$ matrix and contains the eigenvalues of $X$ arranged in decreasing order, *i.e.* the largest eigenvalue will be the element $S_{11}$, the second largest eigenvalue will be the element $S_{22}$, and so on. The eigenvectors in $V$ are arranged such that the first row of $V$ holds the eigenvector correspoding to the eigenvalue in $S_{11}$, the second row of $V$ will hold the eigenvector corresponding to eigenvalue in $S_{22}$, and so on.\n",
    "\n",
    "Once the eigenvectors and eigenvalues have been calculated using SVD, the next step in dimensionality reduction using PCA is to choose the size of the dimension we are going to project our data onto. The size of this dimension is determined by $k$, which tells us the number of principal components we want to use. We can tell the `PCA()` class the number of principal components to return, by setting the parameter `n_components=k`, for some chosen value of $k$, like in the code below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "PCA Parameters: PCA(copy=True, iterated_power='auto', n_components=2, random_state=None,\n",
      "  svd_solver='auto', tol=0.0, whiten=False) \n",
      "\n"
     ]
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "\n",
    "pca = PCA(n_components = 2)\n",
    "\n",
    "print('\\nPCA Parameters:', pca, '\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see `pca`contains the parameters we are going to use for our PCA algorithm. Since the random correlated data we created above is 2D, then in this case, $X$ will have a maximum of 2 eigenvectors. We have chosen $k=2$, so that the `PCA()` class will return both principal components (eigenvectors). We chose $k=2$ because we want to visulaize both principal components in the next section. If we didn't want to visulaize both pricncipal components, but rather perform dimensionality reduction directly, we would have chosen $k=1$, to reduce our 2D data to 1D, as we showed at the beginnig. \n",
    "\n",
    "After we have set the paramters of our PCA algorithm, we now have to pass the data to the `PCA()` class. This is done via the `.fit()` method as shown in the code below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "pca.fit(X_norm);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once the `PCA()` class fits the data through the `.fit()` method it returns an array containing the principal components in the attribute `.components_`, and the corresponding eigenvalues in a 1D array in the attribute `.singular_values_`. Other attributes of the `PCA()` class include `.explained_variance_ratio_` which gives the percentage of variance explained by each of the principal components. In the code below we access the above attributes and display their contents:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Array Containing all Principal Components:\n",
      " [[-0.70710678 -0.70710678]\n",
      " [ 0.70710678 -0.70710678]]\n",
      "\n",
      "First Principal Component: [-0.70710678 -0.70710678]\n",
      "Second Principal Component: [ 0.70710678 -0.70710678]\n",
      "\n",
      "Eigenvalues: [42.39465018 14.23705152]\n",
      "\n",
      "Percentage of Variance Explained by Each Principal Component: [0.89865318 0.10134682]\n"
     ]
    }
   ],
   "source": [
    "print('\\nArray Containing all Principal Components:\\n', pca.components_)\n",
    "print('\\nFirst Principal Component:', pca.components_[0])\n",
    "print('Second Principal Component:', pca.components_[1])\n",
    "print('\\nEigenvalues:', pca.singular_values_)\n",
    "print('\\nPercentage of Variance Explained by Each Principal Component:', pca.explained_variance_ratio_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the first principal component has a corresponding eigenvalue of around 42, while the second principal component has an eigenvalue of around 14. We can also see from the `.explained_variance_ratio_` attribute that the first principal component explains approximately 90% of the variance in the data, while the second principal components only explains around 10%. In general, the principal components with the largest eigenvalues, explain the mayority of the variance. In dimensionality reduction, it is custumary to project your data onto the principal components that explain the mayority of the variance. In this case for example, we would like to project our data onto the first principal component, since it exaplans 90% of the variance in the data. For more inforamtion on Scikit-Learn's `PCA()` class please see the [documentation](http://scikit-learn.org/stable/modules/generated/sklearn.decomposition.PCA.html). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Visualizing The Principal Components\n",
    "\n",
    "Now that we have our principal components, let's visualize them. In the code below we use the `utils.plot_data_with_pca_comp()` function from the `utils` module to calculate the principal components of our random correlated data. The function performs all the steps we have seen above and then plots the resulting principal components along with the data. In order to prevent you from scrolling up and down the notebook to create new random correlated data, I have copied the same code as before so you can change the parameters of the random data here as well.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import utils\n",
    "\n",
    "# Set the default figure size\n",
    "plt.rcParams['figure.figsize'] = [10.0, 6.0]\n",
    "\n",
    "# Set data range\n",
    "data_min = 10\n",
    "data_max = 80\n",
    "\n",
    "# Set the amount of correlation\n",
    "corr = 0.8\n",
    "\n",
    "# Plot the data and the principal components   \n",
    "utils.plot_data_with_pca_comp(corr, data_min, data_max)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Choosing The Number of Components\n",
    "\n",
    "As we saw, the dimension of the lower dimensional surface, $k$, is a free parameter of the PCA algorithm. When working with low dimensional data, choosing the value of $k$ can be easy, for example, when working with 2D data, you can choose $k=1$, to reduce your 2D data to 1D. However, when working with high dimensional data, a suitable value for $k$ is not that clear. For example, suppose you had 1,000-dimensional data, what will be the best choice for $k$? Should we choose $k=500$ to reduce our data from 1,000D to 500D, or we could do better than that and reduce our data to 100D by choosing $k=100$. \n",
    "\n",
    "Usually, the number of principal components, $k$, is chosen depending on how much of the variance of the original data you want to retain. Typically, you choose $k$ such that anywhere from 80% to 99% of the variance of the original data is retained, however you can choose a lower percentage if that is what you desire for your particular application. You check the percentage of the variance of your data that is explained for a given value of $k$ using the `.explained_variance_ratio_` attribute as we saw before. So, in practice what you will do, is to have the `PCA()`class return all the eigenvectors and then add up the elements in the array returned the `.explained_variance_ratio_` attribute until the desired retained variance is reached. For example, if we wanted to retain 98% of the variance in our data we choose $k$ such that the following condition is true:\n",
    "\n",
    "\\begin{equation}\n",
    "\\sum_{i=1}^k P_{i} \\geq 0.98\n",
    "\\end{equation}\n",
    "\n",
    "where $P$ is the array returned the `.explained_variance_ratio_` attribute. So, if you are choosing the value of $k$ manually, you can use the above formula to figure out what percentage of variance was retained for that particular value of $k$. For highly correlated data, it is possible to reduce the dimensions of the data significantly, even if we retain 99% of the variance. \n",
    "\n",
    "\n",
    "# Projected Data\n",
    "\n",
    "Now that we have seen what all the principal components look like, we will now use the `PCA()` class with `n_components = 1` so that we can perform dimensionality reduction. Once we find the vectors (principal component) that span our lower dimensional space, the next part of the dimensionality redcution algorithm is to find the projected values of our data onto that space. We can use the `.transform()` method from the `PCA()` class to apply dimensionalty reduction and project our data points onto the lower dimensional space. In our simple example, $k=1$, so we will only have a principal component to project our data onto. \n",
    "\n",
    "In the code below, we apply PCA with `n_components = 1`  and use the `.transform()` method to project our data points onto a straight line. Finally we plot our projected data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "from sklearn.decomposition import PCA\n",
    "\n",
    "pca = PCA(n_components = 1)\n",
    "\n",
    "pca.fit(X_norm);\n",
    "\n",
    "transformed_data = pca.transform(X_norm)\n",
    "\n",
    "yvals = np.zeros(1000)\n",
    "\n",
    "# Plot the data\n",
    "plt.scatter(transformed_data, yvals, color = 'white', alpha = 0.5, linewidth = 0)\n",
    "ax = plt.gca()\n",
    "ax.set_facecolor('lightslategray')\n",
    "plt.grid()\n",
    "\n",
    "plt.show()"
   ]
  }
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